A ladder makes an angle of 30^circ with the w | vedclass

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

Question

(B) Let the ladder be represented by the hypotenuse of a right-angled triangle formed by the ladder,the wall,and the floor.Let $x$ be the distance of

Vedclass · Accepted Answer

$\frac{3}{2} 	ext{ ft/sec}$

Vedclass · Answer

(B) Let the ladder be represented by the hypotenuse of a right-angled triangle formed by the ladder,the wall,and the floor.Let $x$ be the distance of the man from the wall along the ladder.Let $y$ be the horizontal distance of the man from the wall.The angle between the ladder and the wall is $	heta = 30^\circ$.From trigonometry,the horizontal distance $y$ is given by $y = x \sin(	heta)$.Here,$	heta = 30^\circ$,so $y = x \sin(30^\circ) = x 	imes \frac{1}{2}$.Differentiating with respect to time $t$,we get $\frac{dy}{dt} = \frac{dx}{dt} 	imes \frac{1}{2}$.Given that the rate of climbing the ladder is $\frac{dx}{dt} = 3 	ext{ ft/sec}$.Therefore,the rate at which he approaches the wall is $\frac{dy}{dt} = 3 	imes \frac{1}{2} = \frac{3}{2} 	ext{ ft/sec}$.

$A$ ladder makes an angle of $30^\circ$ with the wall. $A$ man is climbing the ladder at the rate of $3 \text{ ft/sec}$. What is the rate at which he is approaching the wall?

Similar Questions

The equation of motion of a particle is given by $s = 2t^3 - 9t^2 + 12t + 1$,where $s$ and $t$ are measured in $cm$ and $sec$. The time when the particle stops momentarily is

The volume of a sphere is increasing at the rate of $4 \pi \text{ cm}^3/\text{sec}$. When its volume is $288 \pi \text{ cm}^3$, the rate of increase (in $\text{cm/sec}$) in its radius is

If $f(x) = 2x^{2}$,find $\frac{f(3.8) - f(4)}{3.8 - 4}$.

The sides of an equilateral triangle are increasing at the rate of $4 \text{ cm/sec}$. Find the rate at which its area is increasing when the side is $14 \text{ cm}$.

The distance $x$ covered by a particle in time $t$ is given by $x = t^3 - 12t^2 + 6t + 8$. What is the velocity of the particle at the instant when its acceleration is zero?

Vedclass Test Series

Exam Paper Generator

Online Exam Module