Question

(1)
A ball is thrown from a roof top at an angle of ${45}^{\circ }$ above the horizontal. It hits the ground a few seconds later. At what point during its motion, does the ball have greatest speed?

(2)
A ball is thrown from a roof top at an angle of ${45}^{\circ }$ above the horizontal. It hits the ground a few seconds later. At what point during its motion, does the ball have smallest speed?

(3)
A ball is thrown from a roof top at an angle of ${45}^{\circ }$ above the horizontal. It hits the ground a few seconds later. At what point during its motion, does the ball have greatest acceleration?

Answer 1

(1)

Step 1: Draw rough diagram for the motion of the particle


Step 2: Find the point at which the ball has greatest speed.
Let a ball is thrown from a roof top at an angle ${45}^{\circ }$ with speed $u$.
At point $B$ the ball will gain the same speed $u$ and after point $B$ ball moves in direction of force (gravitational force), so its speed increases and will be maximum just before reaching $C$ (ground).

Final answer: just before it hits the ground.

(2)
Step 1: Draw rough diagram for the motion of the particle.


Step 2: Find the point at which the ball has smallest speed.
During upward journey from $O$ to $A$, speed decreases (as ball moves opposite to direction of force i.e., gravitational force) and attains smallest speed at the highest point, i.e., at point $A$.

Final answer: At the highest point reached.

(3)
Step 1: Draw rough diagram for the motion of the particle.


Step 2: Find the point at which the ball has greatest acceleration.
The ball is moving under gravity so, acceleration is constant throughout the journey and is vertically downwards equal to $g$.

Final answer: $a=g=$ constant.