A man on the top of a 40 meter tower directly overhead the road is watching a car moving on a straight road. The car speed makes an angular velocity with respect to the observer in a constant speed of 0.16radian/sec. Find the linear velocity of the car when its position is such that theta=45deg?
draw the right triangle. Let L be the horizontal length from the base of the tower.
If Theta is the angle of depression from the horizontal (check your drawing), then
Using some geometry, it must be the same angle of the angle of elevation from the car.
TanTheta=40/L
L sinTheta=40 cosTheta
taking the derivative..
SinTheta dL/dt+LcosTheta dTheta/dt=-40sinTheta dTheta/dt
Now, the question asks you to solve dL/dt when Theta=45deg and dTheta/dt=.16
L must = 40 also when theta=45 deg, so you have enough to solve it.