Question

Question: A ball is thrown straight up. What are the velocity and acceleration of the ball at the highest point in its path?

(a) $v=0,a=0$.

(b) $v=0,a=9.8\mathrm{m}/{\mathrm{s}}^2$up.

(c) $v=0,a=9.8\mathrm{m}/{\mathrm{s}}^2$down.

(d) $v=9.8\mathrm{m}/\mathrm{s}\mathrm{up},a=0$.

(e) $v=9.8\mathrm{m}/\mathrm{s}\mathrm{down},a=0$.

Short answer

The correct option is (c)$v=0,a=9.8\mathrm{m}/{\mathrm{s}}^2$ down.

Step-by-step solution

Step 1. Definitions of velocity and acceleration of the ball

Velocity denotes the variation in the displacement of the ball with respect to a particular frame of reference and the time taken by the ball.

Acceleration denotes the variation in the velocity of the ball with respect to the required time.

Step 2. Determination of velocity at the highest point

When the ball is thrown upward, it becomes stationary for a very short duration and acquires zero velocity. Then, the ball returns under the effect of gravity.

This way, the distance between the initial and final positions, i.e., displacement, becomes zero.

So, the velocity can be expressed as:

$V=\frac{\mathrm{displacement}}{\mathrm{time}}$

From the above expression, the velocity is zero.

Thus, the velocity at the highest point in the ball’s path is zero.

Step 3. Determination of acceleration at the highest point

When the ball moves upward, the acceleration due to gravity acts on it downward. Due to this, the ball returns to the ground.

The acceleration (a) is equal to the acceleration due to gravity (g).

$$\begin{gathered} a=g \\ a=9.8\mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$

Thus, the acceleration of the ball at the highest point is $9.8\mathrm{m}/{\mathrm{s}}^2$, acting in the downward direction.

Step 4. Determination of the correct option

Option (a) is incorrect because the velocity at the top is zero, but the acceleration is non-zero at$9.8\mathrm{m}/{\mathrm{s}}^2$.

Option (b) is incorrect because the velocity at the highest point is zero, but the acceleration is $9.8\mathrm{m}/{\mathrm{s}}^2$, in the downward direction.

Option (d) is incorrect because the velocity at the highest point is zero, while the acceleration is not.

Option (e) is incorrect because the velocity at the topmost point is not $9.8\mathrm{m}/\mathrm{s}$, and the acceleration is also not $0\mathrm{m}/{\mathrm{s}}^2$.

The velocity at the topmost point is zero, and the acceleration is $9.8\mathrm{m}/{\mathrm{s}}^2$, in the downward direction.

Hence, option (c) is correct.