Aballoon is released 4 feet away from an observer. the balloon is rising vertically at a rate of 3 ft/sec and at the same time the wind is carrying it horizontally away from the observer at a rate of 4 ft/sec. at what speed is the angle of inclination of the observer’s line of sight changing 4 seconds after the balloon is released?

The rate at which the angle of inclination of the observer’s line of sight is changing after 4 seconds is 7 ft/s.

The given parameters;

The displacement of the balloon after 4 seconds is calculated by applying Pythagoras theorem;

a = 3 x 4 = 12 ft

b = (4 x 4) - 4 = 12 ft

find the rate of change of the displacement;

Thus, the rate at which the angle of inclination of the observer’s line of sight is changing after 4 seconds is 7 ft/s.

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0.022 rad/s

Explanation:

Given

balloon is rising at 3 ft/s

wind is blowing horizontally at 4 ft/s

balloon is released 4 feet away from observer

after t sec balloon has moved a distance of 3t vertically and 4t  horizontally

therefore from diagram

differentiate w.r.t time

now at t=4 s

at t=4  s