Question

A spotlight is fixed 4 m from the vertical wall and is rotating at a rate 1 rads^-1. The spot moves horizontally on the wall. Find the speed of the spot on the wall when the spotlight makes an angle of 45^o with the wall.

• A. 4 ms^-1
• B. 6 ms^-1
• C. 8 ms^-1
• D. None of these

Answer 1

Answer: (C)

8 ms^-1

Answer 2

s is the spot light shown in fig. and x is the distance moved by spot in time t

.

From Fig. x/y = tanφ

x = y tan ∆

v = $\frac{dx}{dt} = y\sec^{2}\varphi\frac{d\varphi}{dt}and\frac{d\varphi}{dt} = \omega = 1$v = 4(2) 1(when θ = 45^o, φ = 45⁰) = 8 ms^-1