OneTime: Motion In Two Dimensions - JEE MCQ

Horizontal velocity at point O = u cos α
Horizontal velocity at point P = v sin α

In projectile motion horizontal, component of velocity remains constant throughout the motion 
∴ v sin α = u cos α
⇒ v = u cot α

Time of flight for the ball thrown by pankaj, 
Time of flight for the ball thrown by sudhir,According to problem,

Height of the ball thrown by pankaj,
Height of the thrown by sudhir,

Here we are given velocity of 'A', 
Velocity of 'A', w.r.t. 'B', 

Now,

Hence velocity of B, 

i.e. S of E

v = v₀ sin θ
u = v₀ cos θ

Time of flight depends on vertical component of velocity.

In circular motion we know the velocity vector is tangent to the circle. If a particle moves in a circle with constant angular speed it perform uniform circular motion. In uniform circular motion the tangential acceleration of the particle is zero. The particle moves under radial acceleration only which points to the centre of the circle. Hence the velocity and acceleration vectors are perpendicular to each other.

Change in velocity:

Due to constant velocity along horizontal and vertical downward force of gravity stone will hit the ground following parabolic path.

Horizontal displacement of the bomb AB = Horizontal velocity × time available

Vertical component of velocity of ball at point P

Horizontal component of velocity = initial velocity 

So the speed with which it hits the ground,

and 

⇒ θ = 45º 

It means the ball hits the ground at an angle of 45^∘ to the horizontal.
Height of the table

Horizontal distance travelled by the ball from the edge of table, h = ut = 4 × 0.4 = 1.6 m

For both cases,

Because vertical downward component of velocity will be zero for both the particles.

If initial velocity be doubled then range will become four times.

At the highest point, vertical component of velocity becomes zero so there will be only horizontal velocity and it is perpendicular to the acceleration due to gravity.

when θ = 45º, R_max ∝ u²

when θ = 90º, H_max ∝ u²

 It is clear that,

For these, it is clear that all the four options are correct