A7 ft tall person is walking away from a 20 ft tall lamppost at a rate of 5 ft/sec. assume the scenario can be modeled with right triangles. at what rate is the length of the person's shadow changing when the person is 16 ft from the lamppost?

The rate of change of the shadow length of a person is 2.692 ft/s

Solution:

As per the question:

Height of a person, H = 20 ft

Height of a person, h = 7 ft

Rate = 5 ft/s

Now,

From Fig.1:

b = person's distance from the lamp post

a = shadow length

Also, from the similarity of the triangles, we can write:

Differentiating the above eqn w.r.t t:

Now, we know that:

Rate =

Thus

acceleration = (change in speed) / (time for the change)

change in speed = (20-120)= -100 m/s.

1.5 min = 90 sec

acceleration = -100/90 = -1.11 m/s^2.

we don't care about the 150kg or the 2,500 meters. they don't make any difference.

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