Referring to Example 2-12 Suppose the balloon is descending with a constant speed of 4.2 m/s when the bag of sand comes loose at a height of 35 m. (a) How long is the bag in the air? (b) What is the speed of the bag when it is 15 m above the ground?

Example 2-12 Look out below! a sandbag in free fall

Solution 129IP

Part (a)

Step 1 of 6:

Consider a bag of sand comes to loose from a balloon which descends with a constant speed. The height of the balloon above the ground is given. We are going to find the time taken by the bag to reach the ground.

The initial speed of the bag v0 = 4.2 m/s

The acceleration due to gravity g = 9.81 m/s2

The initial above the ground Δx = 35 m

Step 2 of 6:

The time taken by the bag to reach the could be found only if we know the final speed of the bag. We need to find this value by using the equation motion for constant acceleration. Here the acceleration is given by gravity (a = g). I am taking all the values as positive.

To find the final speed:

The square of the final speed is expressed as

Putting a = g

Step 3 of 6:

Inserting the values and solving for v

The final speed of the sandbag is 26.54 m/s.