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

Question

Exercise 3.22 Part A A 124-kg balloon carrying a 22-kg basket is descending with a constant downward velocity of 18.9 m/s.A 1.0-kg stone is thrown from the basket with an initial velocity of 17.0 m/s perpendicular to the path of the descending balloon, as measured relative to a person rest in the basket. That person sees th ground 17.6 s after it was thrown. Assume that the ballo constant speed of 18.9 m/s How high was the balloon when the rock was thrown out? Express your answer with the appropriate units e stone hit the on continues its downw ard descent with the same ho= 1 Value Units Submit My Answers Give Up Part B How high is the balloon when the rock hits the ground? Express your answer with the appropriate units hiValue Units Submit My Answers Give Up

Explanation / Answer

initial vertical speed=18.9 m/s
initial horizontal speed=17 m/s
time taken = 17.6 seconds
downward acceleration=9.8 m/s^2
then height of the baloon when the rock was thrown=height descended by the rock in 17.6 seconds

=initial vertical speed*time+0.5*acceleration*time^2
=1850.464 m

part B:

as the baloon is descending at constant speed,height descended by it during 17.6 seconds
is given by 17.6*18.9=332.64 m

then the baloon's height when the rock hits the ground=1850.464-332.64=1517.824 m

part C:
horizontal distance covered by the rock in 17.6 seconds=299.2 m
distance between rock and basket=sqrt(1517.824^2+299.2^2)=1547 m

part D:
horizontal velocity =17 m/s

as when the rock starts from the basket, w.r.t to the basket, its initial vertical speed =0
then final vertical speed=0+9.8*17.6=172.48 m/s

part E:
horizontal velocity=17 m/s
vertical velocity=initial speed+acceleration*time=18.9+9.8*17.6=191.38 m/s

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