Motion in a Plane Solved Examples | Physics for JEE Main & Advanced PDF Download

 Page 1


Solved Examples on Motion in a 
Plane 
JEE Mains 
Q1: A projectile is fired with a velocity at right angles to the slope which is 
inclined at an angle ?? with the horizontal. The expression for the range ?? along the 
incline is 
(A) 
?? ?? ?? ?? ?? ???? ? ?? 
(B) 
?? ?? ?? ?? ???? ?? ? ?? 
(C) 
?? ?? ?? ?? ???? ?? ? ?? ?? ???? ? ?? 
(D) 
?? ?? ?? ???? ?? ?? ? ?? 
Ans: (C) Let's solve along plane of incline. 
Time of flight ?? =
2 ?? ?? ?? 
Horizontal range along inclined =
1
2
?? ?? ?? 2
 
? =
1
2
?? ?? ·
4 · ?? 2
?? ?? 2
=
2 ?? 2
· ?? ?? ?? ?? 2
?? ?? = ?? sin ? ?? ; ?? ?? = ?? c os ? ?? ?? =
2 ?? 2
· ?? sin ? ?? ?? 2
c o s
2
? ?? ; ? ?? =
2 ?? 2
tan ? ?? s ec ? ?? ?? 
Q2: A hunter tries to hunt a monkey with a small, very poisonous arrow, blown 
from a pipe with initial speed ?? ?? . The monkey is hanging on a branch of a tree at 
height ?? above the ground. The hunter is at a distance ?? from the bottom of the 
tree. The monkey sees the arrow leaving the blow pipe and immediately lose the 
grip on the tree, falling freely down with zero initial velocity. The minimum initial 
speed ?? ?? of the arrow for hunter to succeed while monkey is in air 
(A) v
?? ( ?? ?? + ?? ?? )
????
 
(B) v
?? ?? ?? ?? ?? + ?? ?? 
(C) v
?? ( ?? ?? + ?? ?? )
?? 
(D) v
?? ?? ?? ?? ?? ?? + ?? ?? 
 
Page 2


Solved Examples on Motion in a 
Plane 
JEE Mains 
Q1: A projectile is fired with a velocity at right angles to the slope which is 
inclined at an angle ?? with the horizontal. The expression for the range ?? along the 
incline is 
(A) 
?? ?? ?? ?? ?? ???? ? ?? 
(B) 
?? ?? ?? ?? ???? ?? ? ?? 
(C) 
?? ?? ?? ?? ???? ?? ? ?? ?? ???? ? ?? 
(D) 
?? ?? ?? ???? ?? ?? ? ?? 
Ans: (C) Let's solve along plane of incline. 
Time of flight ?? =
2 ?? ?? ?? 
Horizontal range along inclined =
1
2
?? ?? ?? 2
 
? =
1
2
?? ?? ·
4 · ?? 2
?? ?? 2
=
2 ?? 2
· ?? ?? ?? ?? 2
?? ?? = ?? sin ? ?? ; ?? ?? = ?? c os ? ?? ?? =
2 ?? 2
· ?? sin ? ?? ?? 2
c o s
2
? ?? ; ? ?? =
2 ?? 2
tan ? ?? s ec ? ?? ?? 
Q2: A hunter tries to hunt a monkey with a small, very poisonous arrow, blown 
from a pipe with initial speed ?? ?? . The monkey is hanging on a branch of a tree at 
height ?? above the ground. The hunter is at a distance ?? from the bottom of the 
tree. The monkey sees the arrow leaving the blow pipe and immediately lose the 
grip on the tree, falling freely down with zero initial velocity. The minimum initial 
speed ?? ?? of the arrow for hunter to succeed while monkey is in air 
(A) v
?? ( ?? ?? + ?? ?? )
????
 
(B) v
?? ?? ?? ?? ?? + ?? ?? 
(C) v
?? ( ?? ?? + ?? ?? )
?? 
(D) v
?? ?? ?? ?? ?? ?? + ?? ?? 
 
Ans: (A) Height of monkey above ground = H -
1
2
gt
2
 Height of arrow above ground =
V
y
t -
1
2
gt
2
 
? At point of contact both are at same height H -
1
2
 gt
2
= V
y
t -
1
2
gt
2
? H = V
y
t ? ?? =
?? ?? ?? 
Now, here ?? = ?? ?? · ?? ; ? ? = ?? ?? ·
?? ?? ?? 
? V
x
= V
y
(
L
H
) 
?? = ?? ?? v
1 +
?? 2
?? 2
( ?? = v ?? ?? 2
- ?? ?? 2
) =
?? ?? ?? v ?? 2
+ ?? 2
 
Let vertical velocity at the time of impact be ?? ?? 
?? ?? = ?? ?? - ???? 
Minimum value of ?? ?? = - ?? ?? 
? ? - ?? ?? = ?? ?? - ????
2 ?? ?? = ???? ; ? ?? =
?? ?? ?? ? ? 2 ?? ?? =
?? · ?? ?? ?? ? ? ?? ?? =
v
????
2
? ? ?? =
1
?? v
????
2
· v ?? 2
+ ?? 2
=
v
?? ( ?? 2
+ ?? 2
)
2 ?? 
Q3: A swimmer swims in still water at a speed = ?? ???? /???? . He enters a ?????? ?? wide 
river, having river flow speed = ?? ???? /???? at point ?? and proceeds to swim at an 
angle of ??????
°
 with the river flow direction. Another point ?? is located directly 
across ?? on the other side. The swimmer lands on the other bank at a point ?? , 
from which he walks the distance ???? with a speed = ?? ???? /???? . The total time in 
which he reaches from ?? to ?? is 
(A) 5 minutes 
(B) 4 minutes 
(C) 3 minutes 
(D) None 
Ans: (B) 
?? ?? = ?? s i n ? 53
°
= 5 ·
4
5
= 4 km /hr
?? ?? = ?? c os ? 127
°
= - 3 km /hr
 
Page 3


Solved Examples on Motion in a 
Plane 
JEE Mains 
Q1: A projectile is fired with a velocity at right angles to the slope which is 
inclined at an angle ?? with the horizontal. The expression for the range ?? along the 
incline is 
(A) 
?? ?? ?? ?? ?? ???? ? ?? 
(B) 
?? ?? ?? ?? ???? ?? ? ?? 
(C) 
?? ?? ?? ?? ???? ?? ? ?? ?? ???? ? ?? 
(D) 
?? ?? ?? ???? ?? ?? ? ?? 
Ans: (C) Let's solve along plane of incline. 
Time of flight ?? =
2 ?? ?? ?? 
Horizontal range along inclined =
1
2
?? ?? ?? 2
 
? =
1
2
?? ?? ·
4 · ?? 2
?? ?? 2
=
2 ?? 2
· ?? ?? ?? ?? 2
?? ?? = ?? sin ? ?? ; ?? ?? = ?? c os ? ?? ?? =
2 ?? 2
· ?? sin ? ?? ?? 2
c o s
2
? ?? ; ? ?? =
2 ?? 2
tan ? ?? s ec ? ?? ?? 
Q2: A hunter tries to hunt a monkey with a small, very poisonous arrow, blown 
from a pipe with initial speed ?? ?? . The monkey is hanging on a branch of a tree at 
height ?? above the ground. The hunter is at a distance ?? from the bottom of the 
tree. The monkey sees the arrow leaving the blow pipe and immediately lose the 
grip on the tree, falling freely down with zero initial velocity. The minimum initial 
speed ?? ?? of the arrow for hunter to succeed while monkey is in air 
(A) v
?? ( ?? ?? + ?? ?? )
????
 
(B) v
?? ?? ?? ?? ?? + ?? ?? 
(C) v
?? ( ?? ?? + ?? ?? )
?? 
(D) v
?? ?? ?? ?? ?? ?? + ?? ?? 
 
Ans: (A) Height of monkey above ground = H -
1
2
gt
2
 Height of arrow above ground =
V
y
t -
1
2
gt
2
 
? At point of contact both are at same height H -
1
2
 gt
2
= V
y
t -
1
2
gt
2
? H = V
y
t ? ?? =
?? ?? ?? 
Now, here ?? = ?? ?? · ?? ; ? ? = ?? ?? ·
?? ?? ?? 
? V
x
= V
y
(
L
H
) 
?? = ?? ?? v
1 +
?? 2
?? 2
( ?? = v ?? ?? 2
- ?? ?? 2
) =
?? ?? ?? v ?? 2
+ ?? 2
 
Let vertical velocity at the time of impact be ?? ?? 
?? ?? = ?? ?? - ???? 
Minimum value of ?? ?? = - ?? ?? 
? ? - ?? ?? = ?? ?? - ????
2 ?? ?? = ???? ; ? ?? =
?? ?? ?? ? ? 2 ?? ?? =
?? · ?? ?? ?? ? ? ?? ?? =
v
????
2
? ? ?? =
1
?? v
????
2
· v ?? 2
+ ?? 2
=
v
?? ( ?? 2
+ ?? 2
)
2 ?? 
Q3: A swimmer swims in still water at a speed = ?? ???? /???? . He enters a ?????? ?? wide 
river, having river flow speed = ?? ???? /???? at point ?? and proceeds to swim at an 
angle of ??????
°
 with the river flow direction. Another point ?? is located directly 
across ?? on the other side. The swimmer lands on the other bank at a point ?? , 
from which he walks the distance ???? with a speed = ?? ???? /???? . The total time in 
which he reaches from ?? to ?? is 
(A) 5 minutes 
(B) 4 minutes 
(C) 3 minutes 
(D) None 
Ans: (B) 
?? ?? = ?? s i n ? 53
°
= 5 ·
4
5
= 4 km /hr
?? ?? = ?? c os ? 127
°
= - 3 km /hr
 
Resultant velocity along x-direction 
= V
R
+ V
x
= 4 - 3 = 1 km /hr 
Time of swim =
 width 
?? ?? =
200
4 ·
5
18
= 180 seconds 
Drift = ?? Result 
× ?? = (
1 × 5
18
) × ( 180 ) = 50 m 
Time of walk =
 Drift 
V
=
50
3 ×
5
18
= 60 second 
Total time = 180 + 60 = 240 s = 4 minutes 
Q4: A boy can throw a stone up to a maximum height of ?? ?? . The maximum 
horizontal distance that the boy can throw the same stone up to will be 
 
(A) ???? v ?? ?? 
(B) ?? ?? ?? 
(C) ???? v ?? ?? 
(D) ???? ?? 
Ans: (D) maximum vertical height =
u
2
2 g
= 10 m Horizontal range of a projectile =
u
2
s i n ? 2 ?? 2 g
 
Range is maximum when ?? = 45
°
 
Maximum horizontal range =
u
2
 g
 
Hence maximum horizontal distance = 20 m. 
Q5: A projectile is given an initial velocity of ( ?? ˆ + ?? ?? ˆ ) ?? / ?? , where ?? ˆ is along the 
ground and ?? ˆ is along the vertical. If = ???? ?? / ?? ?? , the equation of its trajectory is: 
 
(A) ?? = 2 ?? - 5 ?? 2
 
(B) 4 ?? = 2 ?? - 5 ?? 2
 
(C) 4 ?? = 2 ?? - 25 ?? 2
 
(D) ?? = ?? - 5 ?? 2
 
Ans: (A) ?? = ?? ; ?? = 2 ?? - 5 ?? 2
 
Equation of trajectory is ?? = 2 ?? - 5 ?? 2
 
 
Q6: A body of mass ?? ???? has an initial velocity of ?? ?? / ?? along ???? and it is 
subjected to a force of 4 Newton's in ???? direction perpendicular to ???? . The 
distance of the body from ?? after 4 seconds will be 
(a) ???? ?? 
(b) ???? ?? 
(c) ???? ?? 
(d) 25 m 
Ans: (c) Body moves horizontally with constant initial velocity 3 m / s upto 4 seconds ? 
?? = ???? = 3 × 4 = 12 ?? 
Page 4


Solved Examples on Motion in a 
Plane 
JEE Mains 
Q1: A projectile is fired with a velocity at right angles to the slope which is 
inclined at an angle ?? with the horizontal. The expression for the range ?? along the 
incline is 
(A) 
?? ?? ?? ?? ?? ???? ? ?? 
(B) 
?? ?? ?? ?? ???? ?? ? ?? 
(C) 
?? ?? ?? ?? ???? ?? ? ?? ?? ???? ? ?? 
(D) 
?? ?? ?? ???? ?? ?? ? ?? 
Ans: (C) Let's solve along plane of incline. 
Time of flight ?? =
2 ?? ?? ?? 
Horizontal range along inclined =
1
2
?? ?? ?? 2
 
? =
1
2
?? ?? ·
4 · ?? 2
?? ?? 2
=
2 ?? 2
· ?? ?? ?? ?? 2
?? ?? = ?? sin ? ?? ; ?? ?? = ?? c os ? ?? ?? =
2 ?? 2
· ?? sin ? ?? ?? 2
c o s
2
? ?? ; ? ?? =
2 ?? 2
tan ? ?? s ec ? ?? ?? 
Q2: A hunter tries to hunt a monkey with a small, very poisonous arrow, blown 
from a pipe with initial speed ?? ?? . The monkey is hanging on a branch of a tree at 
height ?? above the ground. The hunter is at a distance ?? from the bottom of the 
tree. The monkey sees the arrow leaving the blow pipe and immediately lose the 
grip on the tree, falling freely down with zero initial velocity. The minimum initial 
speed ?? ?? of the arrow for hunter to succeed while monkey is in air 
(A) v
?? ( ?? ?? + ?? ?? )
????
 
(B) v
?? ?? ?? ?? ?? + ?? ?? 
(C) v
?? ( ?? ?? + ?? ?? )
?? 
(D) v
?? ?? ?? ?? ?? ?? + ?? ?? 
 
Ans: (A) Height of monkey above ground = H -
1
2
gt
2
 Height of arrow above ground =
V
y
t -
1
2
gt
2
 
? At point of contact both are at same height H -
1
2
 gt
2
= V
y
t -
1
2
gt
2
? H = V
y
t ? ?? =
?? ?? ?? 
Now, here ?? = ?? ?? · ?? ; ? ? = ?? ?? ·
?? ?? ?? 
? V
x
= V
y
(
L
H
) 
?? = ?? ?? v
1 +
?? 2
?? 2
( ?? = v ?? ?? 2
- ?? ?? 2
) =
?? ?? ?? v ?? 2
+ ?? 2
 
Let vertical velocity at the time of impact be ?? ?? 
?? ?? = ?? ?? - ???? 
Minimum value of ?? ?? = - ?? ?? 
? ? - ?? ?? = ?? ?? - ????
2 ?? ?? = ???? ; ? ?? =
?? ?? ?? ? ? 2 ?? ?? =
?? · ?? ?? ?? ? ? ?? ?? =
v
????
2
? ? ?? =
1
?? v
????
2
· v ?? 2
+ ?? 2
=
v
?? ( ?? 2
+ ?? 2
)
2 ?? 
Q3: A swimmer swims in still water at a speed = ?? ???? /???? . He enters a ?????? ?? wide 
river, having river flow speed = ?? ???? /???? at point ?? and proceeds to swim at an 
angle of ??????
°
 with the river flow direction. Another point ?? is located directly 
across ?? on the other side. The swimmer lands on the other bank at a point ?? , 
from which he walks the distance ???? with a speed = ?? ???? /???? . The total time in 
which he reaches from ?? to ?? is 
(A) 5 minutes 
(B) 4 minutes 
(C) 3 minutes 
(D) None 
Ans: (B) 
?? ?? = ?? s i n ? 53
°
= 5 ·
4
5
= 4 km /hr
?? ?? = ?? c os ? 127
°
= - 3 km /hr
 
Resultant velocity along x-direction 
= V
R
+ V
x
= 4 - 3 = 1 km /hr 
Time of swim =
 width 
?? ?? =
200
4 ·
5
18
= 180 seconds 
Drift = ?? Result 
× ?? = (
1 × 5
18
) × ( 180 ) = 50 m 
Time of walk =
 Drift 
V
=
50
3 ×
5
18
= 60 second 
Total time = 180 + 60 = 240 s = 4 minutes 
Q4: A boy can throw a stone up to a maximum height of ?? ?? . The maximum 
horizontal distance that the boy can throw the same stone up to will be 
 
(A) ???? v ?? ?? 
(B) ?? ?? ?? 
(C) ???? v ?? ?? 
(D) ???? ?? 
Ans: (D) maximum vertical height =
u
2
2 g
= 10 m Horizontal range of a projectile =
u
2
s i n ? 2 ?? 2 g
 
Range is maximum when ?? = 45
°
 
Maximum horizontal range =
u
2
 g
 
Hence maximum horizontal distance = 20 m. 
Q5: A projectile is given an initial velocity of ( ?? ˆ + ?? ?? ˆ ) ?? / ?? , where ?? ˆ is along the 
ground and ?? ˆ is along the vertical. If = ???? ?? / ?? ?? , the equation of its trajectory is: 
 
(A) ?? = 2 ?? - 5 ?? 2
 
(B) 4 ?? = 2 ?? - 5 ?? 2
 
(C) 4 ?? = 2 ?? - 25 ?? 2
 
(D) ?? = ?? - 5 ?? 2
 
Ans: (A) ?? = ?? ; ?? = 2 ?? - 5 ?? 2
 
Equation of trajectory is ?? = 2 ?? - 5 ?? 2
 
 
Q6: A body of mass ?? ???? has an initial velocity of ?? ?? / ?? along ???? and it is 
subjected to a force of 4 Newton's in ???? direction perpendicular to ???? . The 
distance of the body from ?? after 4 seconds will be 
(a) ???? ?? 
(b) ???? ?? 
(c) ???? ?? 
(d) 25 m 
Ans: (c) Body moves horizontally with constant initial velocity 3 m / s upto 4 seconds ? 
?? = ???? = 3 × 4 = 12 ?? 
and in perpendicular direction it moves under the effect of constant force with zero initial 
velocity upto 4 seconds. 
? ?? = ???? +
1
2
( ?? ) ?? 2
= 0 +
1
2
(
?? ?? ) ?? 2
=
1
2
(
4
2
) 4
2
= 16 ?? 
So its distance from ?? is given by ?? = v ?? 2
+ ?? 2
= v ( 12 )
2
+ ( 16 )
2
 
? ? ?? = 20 m 
 
Q7: A man can throw a stone ?? ?? . The maximum height to which he can raise the 
stone is 
(a) ???? ?? 
(b) ???? ?? 
(c) ???? ?? 
(d) ???? ?? 
Ans: (d) The problem is different from problem no. (54). In that problem for a given angle 
of projection range was given and we had find maximum height for that angle. 
But in this problem angle of projection can vary, ?? mi x
=
?? 2
?? = 80 m ? [for ?? = 45
°
 ] 
But height can be maximum when body projected vertically up 
?? max
=
?? 2
s i n
2
? 90
°
2 ?? =
?? 2
2 ?? =
1
2
(
?? 2
?? ) = 40 m 
 
Q8: When the driver of a car A sees a car B moving towards his car and at a 
distance ?? ?? , takes a left turn of ????
°
. At the same instant the driver of the car B 
takes a turn to his right at an angle ????
°
. The two cars collides after two seconds, 
then the velocity (in ?? / ?? ) of the car A and B respectively will be: [assume both 
cars to be moving along same line with constant speed] 
(A) ?? . ?? , ?? . ?? v ?? 
(B) ?? . ?? , ?? . ?? 
(C) ?? . ?? v ?? , ?? . ?? 
(D) None 
Ans: (C)  
?? ?? 1
= ?? ?? 2
? ? ?? 1
sin ? 60
°
= ?? 2
sin ? 30
°
?? 2
= v 3 ?? 1
 
Relative velocity linearly 
= ?? 1
c os ? 60 + ?? 2
c os ? 30 
Page 5


Solved Examples on Motion in a 
Plane 
JEE Mains 
Q1: A projectile is fired with a velocity at right angles to the slope which is 
inclined at an angle ?? with the horizontal. The expression for the range ?? along the 
incline is 
(A) 
?? ?? ?? ?? ?? ???? ? ?? 
(B) 
?? ?? ?? ?? ???? ?? ? ?? 
(C) 
?? ?? ?? ?? ???? ?? ? ?? ?? ???? ? ?? 
(D) 
?? ?? ?? ???? ?? ?? ? ?? 
Ans: (C) Let's solve along plane of incline. 
Time of flight ?? =
2 ?? ?? ?? 
Horizontal range along inclined =
1
2
?? ?? ?? 2
 
? =
1
2
?? ?? ·
4 · ?? 2
?? ?? 2
=
2 ?? 2
· ?? ?? ?? ?? 2
?? ?? = ?? sin ? ?? ; ?? ?? = ?? c os ? ?? ?? =
2 ?? 2
· ?? sin ? ?? ?? 2
c o s
2
? ?? ; ? ?? =
2 ?? 2
tan ? ?? s ec ? ?? ?? 
Q2: A hunter tries to hunt a monkey with a small, very poisonous arrow, blown 
from a pipe with initial speed ?? ?? . The monkey is hanging on a branch of a tree at 
height ?? above the ground. The hunter is at a distance ?? from the bottom of the 
tree. The monkey sees the arrow leaving the blow pipe and immediately lose the 
grip on the tree, falling freely down with zero initial velocity. The minimum initial 
speed ?? ?? of the arrow for hunter to succeed while monkey is in air 
(A) v
?? ( ?? ?? + ?? ?? )
????
 
(B) v
?? ?? ?? ?? ?? + ?? ?? 
(C) v
?? ( ?? ?? + ?? ?? )
?? 
(D) v
?? ?? ?? ?? ?? ?? + ?? ?? 
 
Ans: (A) Height of monkey above ground = H -
1
2
gt
2
 Height of arrow above ground =
V
y
t -
1
2
gt
2
 
? At point of contact both are at same height H -
1
2
 gt
2
= V
y
t -
1
2
gt
2
? H = V
y
t ? ?? =
?? ?? ?? 
Now, here ?? = ?? ?? · ?? ; ? ? = ?? ?? ·
?? ?? ?? 
? V
x
= V
y
(
L
H
) 
?? = ?? ?? v
1 +
?? 2
?? 2
( ?? = v ?? ?? 2
- ?? ?? 2
) =
?? ?? ?? v ?? 2
+ ?? 2
 
Let vertical velocity at the time of impact be ?? ?? 
?? ?? = ?? ?? - ???? 
Minimum value of ?? ?? = - ?? ?? 
? ? - ?? ?? = ?? ?? - ????
2 ?? ?? = ???? ; ? ?? =
?? ?? ?? ? ? 2 ?? ?? =
?? · ?? ?? ?? ? ? ?? ?? =
v
????
2
? ? ?? =
1
?? v
????
2
· v ?? 2
+ ?? 2
=
v
?? ( ?? 2
+ ?? 2
)
2 ?? 
Q3: A swimmer swims in still water at a speed = ?? ???? /???? . He enters a ?????? ?? wide 
river, having river flow speed = ?? ???? /???? at point ?? and proceeds to swim at an 
angle of ??????
°
 with the river flow direction. Another point ?? is located directly 
across ?? on the other side. The swimmer lands on the other bank at a point ?? , 
from which he walks the distance ???? with a speed = ?? ???? /???? . The total time in 
which he reaches from ?? to ?? is 
(A) 5 minutes 
(B) 4 minutes 
(C) 3 minutes 
(D) None 
Ans: (B) 
?? ?? = ?? s i n ? 53
°
= 5 ·
4
5
= 4 km /hr
?? ?? = ?? c os ? 127
°
= - 3 km /hr
 
Resultant velocity along x-direction 
= V
R
+ V
x
= 4 - 3 = 1 km /hr 
Time of swim =
 width 
?? ?? =
200
4 ·
5
18
= 180 seconds 
Drift = ?? Result 
× ?? = (
1 × 5
18
) × ( 180 ) = 50 m 
Time of walk =
 Drift 
V
=
50
3 ×
5
18
= 60 second 
Total time = 180 + 60 = 240 s = 4 minutes 
Q4: A boy can throw a stone up to a maximum height of ?? ?? . The maximum 
horizontal distance that the boy can throw the same stone up to will be 
 
(A) ???? v ?? ?? 
(B) ?? ?? ?? 
(C) ???? v ?? ?? 
(D) ???? ?? 
Ans: (D) maximum vertical height =
u
2
2 g
= 10 m Horizontal range of a projectile =
u
2
s i n ? 2 ?? 2 g
 
Range is maximum when ?? = 45
°
 
Maximum horizontal range =
u
2
 g
 
Hence maximum horizontal distance = 20 m. 
Q5: A projectile is given an initial velocity of ( ?? ˆ + ?? ?? ˆ ) ?? / ?? , where ?? ˆ is along the 
ground and ?? ˆ is along the vertical. If = ???? ?? / ?? ?? , the equation of its trajectory is: 
 
(A) ?? = 2 ?? - 5 ?? 2
 
(B) 4 ?? = 2 ?? - 5 ?? 2
 
(C) 4 ?? = 2 ?? - 25 ?? 2
 
(D) ?? = ?? - 5 ?? 2
 
Ans: (A) ?? = ?? ; ?? = 2 ?? - 5 ?? 2
 
Equation of trajectory is ?? = 2 ?? - 5 ?? 2
 
 
Q6: A body of mass ?? ???? has an initial velocity of ?? ?? / ?? along ???? and it is 
subjected to a force of 4 Newton's in ???? direction perpendicular to ???? . The 
distance of the body from ?? after 4 seconds will be 
(a) ???? ?? 
(b) ???? ?? 
(c) ???? ?? 
(d) 25 m 
Ans: (c) Body moves horizontally with constant initial velocity 3 m / s upto 4 seconds ? 
?? = ???? = 3 × 4 = 12 ?? 
and in perpendicular direction it moves under the effect of constant force with zero initial 
velocity upto 4 seconds. 
? ?? = ???? +
1
2
( ?? ) ?? 2
= 0 +
1
2
(
?? ?? ) ?? 2
=
1
2
(
4
2
) 4
2
= 16 ?? 
So its distance from ?? is given by ?? = v ?? 2
+ ?? 2
= v ( 12 )
2
+ ( 16 )
2
 
? ? ?? = 20 m 
 
Q7: A man can throw a stone ?? ?? . The maximum height to which he can raise the 
stone is 
(a) ???? ?? 
(b) ???? ?? 
(c) ???? ?? 
(d) ???? ?? 
Ans: (d) The problem is different from problem no. (54). In that problem for a given angle 
of projection range was given and we had find maximum height for that angle. 
But in this problem angle of projection can vary, ?? mi x
=
?? 2
?? = 80 m ? [for ?? = 45
°
 ] 
But height can be maximum when body projected vertically up 
?? max
=
?? 2
s i n
2
? 90
°
2 ?? =
?? 2
2 ?? =
1
2
(
?? 2
?? ) = 40 m 
 
Q8: When the driver of a car A sees a car B moving towards his car and at a 
distance ?? ?? , takes a left turn of ????
°
. At the same instant the driver of the car B 
takes a turn to his right at an angle ????
°
. The two cars collides after two seconds, 
then the velocity (in ?? / ?? ) of the car A and B respectively will be: [assume both 
cars to be moving along same line with constant speed] 
(A) ?? . ?? , ?? . ?? v ?? 
(B) ?? . ?? , ?? . ?? 
(C) ?? . ?? v ?? , ?? . ?? 
(D) None 
Ans: (C)  
?? ?? 1
= ?? ?? 2
? ? ?? 1
sin ? 60
°
= ?? 2
sin ? 30
°
?? 2
= v 3 ?? 1
 
Relative velocity linearly 
= ?? 1
c os ? 60 + ?? 2
c os ? 30 
=
?? 1
2
+
v 3
2
?? 2
 
They collide in 2 second 
? ? (
?? 1
2
+
v 3
2
?? 2
) ( 2 ) = 30
?? 1
+ v 3 ?? 2
= 30
?? 2
= v 3 ?? 1
? ? ?? 1
+ v 3 ( v 3 ?? 1
) = 30
? ? ?? 1
= 7 . 5 ms
- 1
?? 2
= 7 . 5 ms
- 1
?? 1
 is velocity of ?? ?? 2
 is velocity of A 
 
Q9: A particle is projected with a certain velocity at an angle ?? above the 
horizontal from the foot of a given plane inclined at an angle of ????
°
 to the 
horizontal. If the particle strikes the plane normally, then equals 
(A) ???? ?? - ?? ? ( ?? / ?? ) 
(B) ???? ?? - ?? ? ( ?? / ?? ) 
(C) ???? ?? - ?? ? ( ?? / v ?? ) 
(D) ???? ?? - ?? ? ?? 
Ans: (D) Lets solve the problem taking along plane as ?? -axis and perpendicular to plane 
as ?? -axis