A person of height 1.6 m is walking away fro | vedclass

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

Question

(C) Let $x$ be the distance of the person from the lamp post and $y$ be the distance of the tip of the shadow from the lamp post. By similar triangles

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(C) Let $x$ be the distance of the person from the lamp post and $y$ be the distance of the tip of the shadow from the lamp post. By similar triangles,we have:$\frac{4}{y} = \frac{1.6}{y - x}$$4(y - x) = 1.6y$$4y - 4x = 1.6y$$2.4y = 4x$$x = 0.6y$Differentiating with respect to time $t$:$\frac{dx}{dt} = 0.6 \frac{dy}{dt}$Given $\frac{dx}{dt} = 60 \ cm \ s^{-1}$,we have:$60 = 0.6 \frac{dy}{dt}$$\frac{dy}{dt} = \frac{60}{0.6} = 100 \ cm \ s^{-1}$The speed of the tip of the shadow with respect to the person is given by $v_{tip/person} = \frac{dy}{dt} - \frac{dx}{dt} = 100 - 60 = 40 \ cm \ s^{-1}$.

Similar Questions

All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.

$A$ car moves towards north at a speed of $54 \,km/h$ for $1 \,h$. Then it moves eastward with the same speed for the same duration. The average speed and velocity of the car for the complete journey is ..........

The displacement $x$ of a particle depends on time $t$ as $x = \alpha t^2 - \beta t^3$.

State whether the following statements are true or false:
$(a)$ Velocity can change without a change in speed.
$(b)$ The total distance covered by a freely falling body in a given time is directly proportional to the time.
$(c)$ $A$ particle is a point object that possesses dimensions.

Vedclass Test Series

Exam Paper Generator

Online Exam Module