Question

A hot-air balloon rises from ground level at a constant velocity of 3.0 m/s. One minute after liftoff, a sandbag is dropped accidentally from the balloon. Calculate (a) the time it takes for the sandbag to reach the ground and (b) the velocity of the sandbag when it hits the ground.

a) (a) 15 s, (b) 3.0 m/s
b) (a) 30 s, (b) 3.0 m/s
c) (a) 15 s, (b) 30 m/s
d) (a) 30 s, (b) 30 m/s

Answer 1

The sandbag will have a velocity of 3.0 m/s when it is dropped from the hot-air balloon. It will take approximately 1.43 seconds for the sandbag to reach the ground.

Step-by-step explanation:

When a hot-air balloon is rising at a constant velocity, the upward velocity of the balloon is equal to the downward force of gravity. This means that the velocity of the sandbag when it is dropped will also be 3.0 m/s.

To calculate the time it takes for the sandbag to reach the ground, we can use the equation h = 1/2 * g * t^2, where h is the height, g is the acceleration due to gravity, and t is the time. In this case, the initial height of the sandbag is the height of the balloon at the time it is dropped, and the final height is 0 (ground level). Plugging in the values, we get:

0 = 1/2 * 9.8 * t^2

Simplifying the equation, we find that it takes approximately 1.43 seconds for the sandbag to reach the ground.