A 124-kg balloon carrying a 22-kg basket is descending with a constant downward

Question

A 124-kg balloon carrying a 22-kg basket is descending with a constant downward velocity of 10.7 m/s A 1.0-kg stone is thrown from the basket with an initial velocity of 11.8 m/s perpendicular to the path of the descending balloon, as measured relative to a person at rest in the basket. The person in the basket sees the stone hit the ground 5.00 s after being thrown. Assume that the balloon continues its downward descent with the same constant speed of 10.7 m/s .

How high was the balloon when the rock was thrown out?

How high is the balloon when the rock hits the ground?

At the instant the rock hits the ground, how far is it from the basket?

Just before the rock hits the ground, find its horizontal and vertical velocity components as measured by an observer at rest on the ground.

Explanation / Answer

weight of the ballon + basket = 124 +2 = 126 kg

speed of the ballon = 10.7 m/s downward

when the stone was thrown , it has an horizontal velocit ux = 11.8 m/s

                                                              vertical vel           uy = 10.7 m/s , same as that of balloon

in vertical direction height

h = uy t +gt2/2   , given t= 5, the sotne hit the ground 5 secs aftre thrown

     = 10.7*5 +0.5*9.8*52   = 176 m , height of the ballon when the stone is thrown.

the rock hit the gorund aftre 5 s

The ballon descend 10.7 *5 = 53.5 m by the time the rock hit the ground

height of the balloon = 176-53.5 = 122.5 m

The rock has an horizontal velocity = 11.8 m

time t =5 s to hit the ground

distance traveled       = 11.8 *5 = 59.0 m , away from the basket

jsuet before the rock hits the ground

horizontal vel = 11.8 m/s , same as intial vel. no external force in horizontal

vertical vel Uy-fin = uy +gt = 10.7 +9.8*5 = 59.7 m/s

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