a) A 16 ft ladder leans against a wall. The bottom of the ladder is 5 ft from th

Question

a) A 16 ft ladder leans against a wall. The bottom of the ladder is 5 ft from the wall at time t=0 and slides away from the wall at a rate of 3 ft/s. Find the velocity of the top of the ladder at time t=1.

b) The speed of sound at seal level using the standard atmosphere is about 340.29 meters per second. There are 3.280840 feet in one meter. Using the assumptions of this model, find the angle between the ladder and the ground at the time that the top of the ladder breaks the speed of sound.

c) The speed of light is about 299,792,458 meters per second. There are still 3.280840 feet in one meter. Using the assumptions of this model, find the angle between the ladder and the ground at the time that the top of the ladder moves at the speed of light.

Explanation / Answer

a)Let the height of the ladder = h

The distance of the bottom of the ladder from the wall = 3t + 5

256 = y^2+(5+3t)^2
0 = 2ydy/dt + 6(5+3t)
dy/dt =-[15+9t]/y
When t = 1
y^2 = 256-64= 192
y = sqrt(192)
dy/dt = -24/sqrt(192) = -1.732 ft/s

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