A point moves straight up a vertical line so that its height (in meters) above the…

MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

A point

P

moves straight up a vertical line so that its height

y

(in meters) above the ground increases at a constant rate of

2.5\,\text{m/s}

. An observer stands

a

meters away from the foot of that vertical line, where

a > 0

is constant. (a) Derive an expression for

\frac{d\theta}{dt}

, the rate of change of the observer’s angle of elevation

\theta

, in terms of

a

and

y

. (b) Evaluate

\frac{d\theta}{dt}

(in

\text{rad/s}

) when

a = 25\,\text{m}

and

y = 7\,\text{m}