Important Formulas: Motion in a Plane | Physics Class 11 - NEET PDF Download

 Page 1


PROJECTILE MOTION & VECTORS
Time of flight : T =
g
sin u 2 ?
Horizontal range : R = 
g
2 sin u
2
?
Maximum height  : H = 
g 2
sin u
2 2
?
Trajectory equation (equation of path) :
y = x tan ?  – 
?
2 2
2
cos u 2
gx
 = x tan ? (1 – 
R
x
)
Projection on an inclined plane
y
x
?
?
Up the Incline Down the Incline 
Range 
?
? ? ? ?
2
2
cos g
) cos( sin u 2
 
?
? ? ? ?
2
2
cos g
) cos( sin u 2
 
Time of flight 
?
?
cos g
sin u 2
 
?
?
cos g
sin u 2
 
Angle of projection with 
incline plane for maximum 
range 
2 4
?
?
?
 
2 4
?
?
?
 
Maximum Range 
) sin 1 ( g
u
2
? ?
 
) sin 1 ( g
u
2
? ?
 
RELATIVE MOTION
B A AB
v v ) B to respect with A of velocity ( v
? ? ?
? ?
B A AB
a a ) B to respect with A of on accelerati ( a
? ? ?
? ?
Relative motion along straight line -
A B BA
x x x
? ? ?
? ?
Page 2


PROJECTILE MOTION & VECTORS
Time of flight : T =
g
sin u 2 ?
Horizontal range : R = 
g
2 sin u
2
?
Maximum height  : H = 
g 2
sin u
2 2
?
Trajectory equation (equation of path) :
y = x tan ?  – 
?
2 2
2
cos u 2
gx
 = x tan ? (1 – 
R
x
)
Projection on an inclined plane
y
x
?
?
Up the Incline Down the Incline 
Range 
?
? ? ? ?
2
2
cos g
) cos( sin u 2
 
?
? ? ? ?
2
2
cos g
) cos( sin u 2
 
Time of flight 
?
?
cos g
sin u 2
 
?
?
cos g
sin u 2
 
Angle of projection with 
incline plane for maximum 
range 
2 4
?
?
?
 
2 4
?
?
?
 
Maximum Range 
) sin 1 ( g
u
2
? ?
 
) sin 1 ( g
u
2
? ?
 
RELATIVE MOTION
B A AB
v v ) B to respect with A of velocity ( v
? ? ?
? ?
B A AB
a a ) B to respect with A of on accelerati ( a
? ? ?
? ?
Relative motion along straight line -
A B BA
x x x
? ? ?
? ?
CROSSING RIVER
A boat or man in a river always moves in the direction of resultant velocity
of velocity of boat (or man) and velocity of river flow.
1. Shortest Time :
   
2. Shortest Path :
velocity along the river,  v
x
 = 0
and velocity perpendicular to river  v
y
 = 
2
R
2
mR
v v ?
The net speed is given by v
m
 = 
2
R
2
mR
v v ?
at an angle of 90º with the river direction.
velocity v
y
 is used only to cross the river,
Page 3


PROJECTILE MOTION & VECTORS
Time of flight : T =
g
sin u 2 ?
Horizontal range : R = 
g
2 sin u
2
?
Maximum height  : H = 
g 2
sin u
2 2
?
Trajectory equation (equation of path) :
y = x tan ?  – 
?
2 2
2
cos u 2
gx
 = x tan ? (1 – 
R
x
)
Projection on an inclined plane
y
x
?
?
Up the Incline Down the Incline 
Range 
?
? ? ? ?
2
2
cos g
) cos( sin u 2
 
?
? ? ? ?
2
2
cos g
) cos( sin u 2
 
Time of flight 
?
?
cos g
sin u 2
 
?
?
cos g
sin u 2
 
Angle of projection with 
incline plane for maximum 
range 
2 4
?
?
?
 
2 4
?
?
?
 
Maximum Range 
) sin 1 ( g
u
2
? ?
 
) sin 1 ( g
u
2
? ?
 
RELATIVE MOTION
B A AB
v v ) B to respect with A of velocity ( v
? ? ?
? ?
B A AB
a a ) B to respect with A of on accelerati ( a
? ? ?
? ?
Relative motion along straight line -
A B BA
x x x
? ? ?
? ?
CROSSING RIVER
A boat or man in a river always moves in the direction of resultant velocity
of velocity of boat (or man) and velocity of river flow.
1. Shortest Time :
   
2. Shortest Path :
velocity along the river,  v
x
 = 0
and velocity perpendicular to river  v
y
 = 
2
R
2
mR
v v ?
The net speed is given by v
m
 = 
2
R
2
mR
v v ?
at an angle of 90º with the river direction.
velocity v
y
 is used only to cross the river,
therefore time to cross the river, t = 
y
v
d
 = 
2
R
2
mR
v v
d
?
and velocity v
x
 is zero, therefore, in this case the drift should be zero.
? v
R
 – v
mR
 sin ? = 0 or v
R
 = v
mR
 sin ?
or ? = sin
–1
 
?
?
?
?
?
?
?
?
mR
R
v
v
RAIN PROBLEMS
Rm
v
?
 = 
R
v
?
 – 
m
v
?
or v
Rm
 = 
2
m
2
R
v v ?