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

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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 $v_{tip/person} = \frac{dy}{dt} - \frac{dx}{dt} = 100 - 60 = 40 \ cm \ s^{-1}$.

Column $I$	Column $II$
$(A)$ Constant positive acceleration	$(p)$ Speed may increase
$(B)$ Constant negative acceleration	$(q)$ Speed may decrease
$(C)$ Constant displacement	$(r)$ Speed is zero
$(D)$ Constant slope of $a-t$ graph	$(s)$ Speed must increase

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Which one of the following statements is wrong?

The engine of a motorcycle can produce a maximum acceleration $5 \, m/s^2$. Its brakes can produce a maximum retardation $10 \, m/s^2$. What is the minimum time in which it can cover a distance of $1.5 \, km$?

Match the following columns.

Column $I$ Column $II$

$(A)$ Constant positive acceleration $(p)$ Speed may increase

$(B)$ Constant negative acceleration $(q)$ Speed may decrease

$(C)$ Constant displacement $(r)$ Speed is zero

$(D)$ Constant slope of $a-t$ graph $(s)$ Speed must increase

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