Featured Deals:
Top Path Light
A street light is mounted at the top of a 15ft-tall pole. A man 6ft tall walks away from the pole with a speed?
A street light is mounted at the top of a 15ft-tall pole. A man 6ft tall walks away from the pole with a speed of 5ft/s along a straight path. How fast is the tip of his shadow moving when he is 40 ft from the pole?
please show work.
ty
..........................|
..........................|
...........|..............|
...........|..............| 15 '
T-------|------------
man pole
Let x be the distance between the man and the pole.
dx/dt=5
Let y be the distance between the man and the tip of his shadow (length of the shadow)
Let x+y = z (the distance between the tip of the shadow and the pole)
By using similar triangles,
z/15 =x / (15-6)
z/15 = x/9
z=(15/9) x
z=(5/3)x
dz/dt = (5/3) dx/dt
dz/dt = (5/3)(5)=25/3=8 1/3
Regardless of how far he is from the pole, the tip of his shadow is moving at a rate of 8 1/3 ft /s
Current EBay auctions for Top Path Light
