Question

Suppose that a passenger intent on lunch during his first ride in a hot-air balloon accidently drops an apple over the side during the balloon’s liftoff. At the moment of the apple’s release, the balloon is accelerating upward with a magnitude of $\mathbf{4}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{m}\mathbf{/}{\mathbf{s}}^{\mathbf{2}}$and has an upward velocity of 2 m / s magnitude. What are the (a) magnitude and (b) direction of the acceleration of the apple just after it is released? (c) Just then, is the apple moving upward or downward, or is it stationery? (d) What is the magnitude of its velocity just then? (e) In the next few moments, does the speed of the apple increase, decrease, or remain constant?

Short answer

1. The magnitude of the acceleration is$9.8\mathrm{m}/{\mathrm{s}}^2$
2. The direction of acceleration is downward
3. Apple is moving upward
4. The magnitude of velocity is 2 m / s
5. Speed of apple will decrease

Step-by-step solution

Identification of given data

The given data can be listed below,

• The upward acceleration is,$\mathrm{a}=4\mathrm{m}/{\mathrm{s}}^2$
• The upward velocity is, v= 2 m/s.

Significance of gravitational force

It deals with the acceleration due to gravity. This gravitation is caused by the gravitational attraction forces.

(a) To find the magnitude of acceleration

When the apple is released, it is only under the influence of gravitational force. It is no longer subject to a hot-air balloon. Thus, the acceleration has a magnitude of $\mathrm{a}=9.8\mathrm{m}/{\mathrm{s}}^2$.

(b) To find the direction of acceleration

Since it is under the influence of gravitational acceleration which acts downward, the direction of acceleration is downward.

(c) To find the direction of the apple

When the apple is released, it has an initial upward velocity which is the velocity of a hot-air balloon also. Thus, the apple is moving upward direction.

(d) To find the magnitude of the velocity

Since the ball maintains the hot-air balloon’s velocity, the magnitude of the velocity is 2 m/s

(e) To find the speed of the apple

Because the acceleration is working downward while the apple is moving upward, the apple's speed will decrease in the coming moments. As a result, the apple's speed will drop until it hits zero, at which point it will begin to increase in the reverse direction.