A hot air balloon is is drifting in level flight due east at 2.5 m/s due to a li

Question

A hot air balloon is is drifting in level flight due east at 2.5 m/s due to a light wind. The pilot suddenly notices that the balloon must gain 24 m of altitude in order to clear the top of a hill 120m to the east. (a) How much time does the pilot have to make the altitude change without crashing into the hill? (b) What minimum, constant, upward acceleration is needed in order to clear the hill? (c) What are the horizontal and vertical components of the balloons velocity at the instant it clears the top of the hill?

Explanation / Answer

a) The hill is 120 m far. Speed of Hot air balloon =2.5m/s

Time to pilot to avoid crashing = 120/2.5 = 48 seconds.

b) using S =ut +0.5at2

U = 0 because the ballon was moving in horizontal direction. Now pilot will lift it up therefore S=24m

24=0.5a482

a=0.021m/s2

c) vertical component v = u+at

V=at = 0.021x48 = 1m/S

Horizontal component = 2.5 m/s as given..

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