Exercise 3.22 A 124-kg balloon carrying a 22-kg basket is descending with a cons

Question

Exercise 3.22 A 124-kg balloon carrying a 22-kg basket is descending with a constant downward velocity of 17.7 m/s. A 1.0-kg stone is thrown from the basket with an initial velocity of 19.0 m/s perpendicular to the path of the descending balloon, as measured relative to a person at rest in the basket. That person sees the stone hit the ground 11.9 s after it was thrown. Assume that the balloon continues its downward descent with the same constant speed of 17.7 m/s . Part B How high is the balloon when the rock hits the ground? Express your answer with the appropriate units.

Explanation / Answer

Initial horizontal velocity of stone = 19.0 m/s
Initial Vertical velocity of stone = 17.7 m/s downwards

Vertical acceleration of stone = 9.8m/s^2 downwards
Time taken by the stone to reach ground = 11.9s

Distance moved by stone in 11.9 seconds =
S = 17.7 * 11.9 + 0.5 * 9.8 * 11.9^2
S = 904.5 m
This is the height of Balloon when the stone was thrown.

Now.
Distance travelled by balloon in 11.9 s
Distance = velocity * time
Distance = 17.7 * 11.9
Distance = 210.6 m

Height of Balloon when stone hits the ground = 904.5 - 210.6 m
Height of Balloon when stone hits the ground = 694 m

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