Question

An observer is 31m above the ground floor of a large hotel atrium looking at a glass-enclosed elevator shaft that is 22m horizontally from the observer. The angle of elevation of the elevator is the angle of the observer's line of sight makes with the horizontal (it may be positive or negative). Assuming that the elevator rises at a rate of 3/ms, what is the rate of change of the angle of elevation when the elevator is 20 m above the ground? When the elevator is 53m above the ground?

please show work

Answer 1

see the related questions below. The first is the identical problem -- just change the numbers.

Answer 2

not enough detail for me to solve it in other one.

Answer 3

of course there is...

when the elevator is x meters up,

tanθ = (x-31)/22

So,

sec^2θ dθ/dt = 1/22 dx/dt

when x=20, tanθ = -11/22, so sec^2θ = 5/4

5/4 dθ/dt = 1/22 (3)
dθ/dt = 55/6 m/s

Is one of the steps unclear?