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?
1 answer:
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
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