I assume you made a diagram.
at a given time of t seconds, let her distance from the lamp be x ft, let the length of her shadow be y ft
by ratios,
6/y = 16/(x+y)
16y = 6x+6y
10y = 6x
5y = 3x
5dy/dt = 3dx/dt
dy/dt = (3/5)(8) = 24/5 ft/s
her shadow is increasing at a constant rate of 24/5 ft/s, no matter where she is
the tip of her shadow is moving at (8 + 24/5)
or 64/5 ft/s
A street light is at the top of a 16 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 8 ft/sec along a straight path. How fast is the tip of her shadow moving along the ground when she is 30 ft from the base of the pole?
How fast is the length of her shadow increasing?
1 answer
1 answer