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

weather forecasts are done by collecting data about the current state of the atmosphere mainly the temperature, humidity and wind and using meteorology, to determine the atmosphere that evolves over time. the h and l mean the high and low pressure. the red strip is a warm front. the blue strip is a cold front. the blue and red strip is a stationary front. the purple strip is a occluded front.

explanation:

be subject to a force andchange its motion