A thief in a stolen car passes through a police check post at his top speed of $$90kmh-1$$. A motorcycle cop, reacting after $$2$$ s, accelerates from rest at $$5$$ $$ms-2$$. His top speed being $$108kmh-1$$. Find the maximum separation between policemen and thief.

Question

A thief in a stolen car passes through a police check post at his top speed of $$90kmh-1$$. A motorcycle cop, reacting after $$2$$ s, accelerates from rest at $$5$$ $$ms-2$$. His top speed being $$108kmh-1$$. Find the maximum separation between policemen and thief.

Infinity Learn · Accepted Answer

$$90$$ $$km/h=90$$×$$518=25$$ $$m/s108$$ $$km/h=108$$×$$518=30$$ $$m/sAt$$ maximum separation their velocities are same.∴ Velocity of motorcycle $$=25$$ $$m/sorat$$ $$=25or$$ $$t=5$$ sBut thief has travelled up to $$7$$ s.$$s1=$$ displacement of $$thief=v1t1=25$$×$$7=175$$ $$ms2=$$ displacement of $$motorcycle=12$$×$$a2t22=12$$×$$5$$×$$(5)2=62.5$$ m∴ Maximum $$separation=s1-s2=112.5$$ m

A thief in a stolen car passes through a police check post at his top speed of $90 {kmh}^{- 1}$ . A motorcycle cop, reacting after $2 s$ , accelerates from rest at $5 {ms}^{- 2}$ . His top speed being $108 {kmh}^{- 1}$ . Find the maximum separation between policemen and thief.

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A thief in a stolen car passes through a police check post at his top speed of 90kmh-1. A motorcycle cop, reacting after 2 s, accelerates from rest at 5 ms-2. His top speed being 108kmh-1. Find the maximum separation between policemen and thief.

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

A thief in a stolen car passes through a police check post at his top speed of $90 {kmh}^{- 1}$ . A motorcycle cop, reacting after $2 s$ , accelerates from rest at $5 {ms}^{- 2}$ . His top speed being $108 {kmh}^{- 1}$ . Find the maximum separation between policemen and thief.