Respuesta :
Answer:
The length of her shadow is changing at the rate -2 m/s
Explanation:
Let the height oh the street light, h = 22 ft
Let the height of the woman, w = 5.5 ft
Horizontal distance to the street light = l
length of shadow = x
h/w = (l + x)/x
22/5.5 = (l + x)/x
4x = l + x
3x = l
x = 1/3 l
taking the derivative with respect to t of both sides
dx/dt = 1/3 dl/dt
dl/dt = -6 ft/sec ( since the woman is walking towards the street light, the value of l is decreasing with time)
dx/dt = 1/3 * (-6)
dx/dt = -2 m/s
Answer:
Explanation:
By applying similar triangles rule,
22/5.5 = (x + s)/s
s = 5.5/22 × (x + s)
ds/dt = 5.5/22 × (dx/dt + ds/dt)
16.5/22 × ds/dt = 5.5/22 × dx/dt
16.5/22 × ds/dt = 5.5/22 × -6
ds/st = -2 ft/s.
