Question

A 6 ft tall person walks away from a 10 ft lamppost at a constant rate of 5 ft/s. What is the rate (in ft/s) that the tip of the shadow moves away from the pole when the person is 15 ft away from the pole?

Answer 1

Answer:

12.5 ft/s

Explanation:

Height of person = 6 ft

height of lamp post = 10 ft

According to the question,

dx / dt = 5 ft/s

Let the rate of tip of the shadow moves away is dy/dt.

According to the diagram

10 / y = 6 / (y - x)

10 y - 10 x = 6 y

y = 2.5 x

Differentiate both sides with respect to t.

dy / dt = 2.5 dx / dt

dy / dt = 2.5 (5) = 12.5 ft /s

Answer 2

When the person is 15 ft away from the pole, the rate is 7.5 ft/s.

Resultant displacement

The resultant displacement is calculated as follows;

$R^2 = 6^2 + 10^2\\\\R = 11.6$

Rate of change of the displacement

10 ft ------ 5 ft

15 ft ------- ?

= (15 x 5)/10

= 7.5 ft/s

Thus, when the person is 15 ft away from the pole, the rate is 7.5 ft/s.

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