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Fbp12 Camera falling from a descending balloon

You are descending in a balloon at a constant velocity of 4 m/s and at a height of 20 m you drop your binoculars.

How long does it take your binoculars to reach the ground?

Where is the balloon when your binoculars hit the ground?

How long does it take the balloon to reach the ground?

How fast are the binoculars moving when they hit the ground?

Diagram the problem with the origin of the coordinate system at the point where you drop the binoculars and take the positive direction down.

Use equation (1) to find the time. Remember to watch the signs closely!

Removing the units and rearranging.

with solution

It takes 1.6 s for the binoculars to reach the ground.

In 1.6 s the balloon has descended (4 m/s)(1.6 s) = 6.4 m and is 13.6 m above the ground.

Descending at the rate of 4 m/s it takes the balloon 5 s to reach the ground.

The velocity of the binoculars as they strike the ground is from equation (4).