A man of height 1.8 m is moving away from a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $AB$ be the lamp post of height $4.5 \ m$ and $PQ$ be the man of height $1.8 \ m$. Let the man be at a distance $y$ from the lamp post,so $QB

Vedclass · Accepted Answer

$0.8$

Vedclass · Answer

(B) Let $AB$ be the lamp post of height $4.5 \ m$ and $PQ$ be the man of height $1.8 \ m$. Let the man be at a distance $y$ from the lamp post,so $QB = y$. Let the length of the shadow be $x$,so $CQ = x$.From similar triangles $	riangle AB C$ and $	riangle PQC$,we have:$\frac{PQ}{AB} = \frac{CQ}{CB}$$\frac{1.8}{4.5} = \frac{x}{x + y}$$\frac{2}{5} = \frac{x}{x + y}$$2(x + y) = 5x$$2x + 2y = 5x$$3x = 2y$$x = \frac{2}{3}y$Differentiating with respect to time $t$:$\frac{dx}{dt} = \frac{2}{3} \frac{dy}{dt}$Given that the man is moving away at $\frac{dy}{dt} = 1.2 \ m/sec$,we have:$\frac{dx}{dt} = \frac{2}{3} 	imes 1.2 = 0.8 \ m/sec$.Thus,the shadow is lengthening at a rate of $0.8 \ m/sec$.

$A$ man of height $1.8 \ m$ is moving away from a lamp post at the rate of $1.2 \ m/sec$. If the height of the lamp post is $4.5 \ m$,then the rate at which the shadow of the man is lengthening is .......... $m/sec$.

Similar Questions

$A$ point is moving along the curve $y^3 = 27x$. The interval in which the abscissa changes at a slower rate than the ordinate is

The rate of change of the volume of the sphere with respect to its surface area $S$ is . . . . . . .

If the volume of a spherical balloon is increasing at the rate of $900 \ cm^3/sec$,then find the rate of change of the radius of the balloon at the instant when the radius is $15 \ cm$ (in $cm/sec$).

The distance $s$ in meters travelled by a particle in $t$ seconds is given by $s = \frac{2 t^3}{3} - 18 t + \frac{5}{3}$. The acceleration when the particle comes to rest is (in $m/s^2$)

The radius of a circle is increasing at the rate of $0.7 \, cm/s$. What is the rate of increase of its circumference?

Vedclass Test Series

Exam Paper Generator

Online Exam Module