Question

a car is moving with a constant speed of 40 km per hour towards north at the same instant scooter which is at a distance of 5 km from the car moves towards the East with 30 kilometre per hour as shown in the figure find the minimum separation between car and scooter

Answer 1

Answer:

75 Is The Correct Answer

Answer 2

Answer: Minimum separation between car and scooter is 3 km

Explanation:

Speed of car moving towards north = 40 km/hr

Distance travelled in time t hours = 40t km

Speed of scooter moving towards east = 30 km/hr

Distance travelled in time t hours = 30t km

After time t hours,

Horizontal separation between car and scooter =  30t

Vertical separation between car and scooter =  | 5 - 40t |

Net separation ⇒ S = $\sqrt{(30t)^{2} +(5-40t)^{2} }$

At minimum separation $\frac{dS}{dt} = 0$

Therefore,

⇒ 2(30t)(30) + 2(5-40t)(-40) = 0

⇒ 90t - 20 + 160t = 0

⇒ 250t = 20

$t = \frac{2}{25}$

Minimum separation = $\sqrt{(30*\frac{2}{25} )^{2} +(5-40*\frac{2}{25} )^{2} }$

Minimum separation = $\sqrt{(\frac{60}{25} )^{2} +(\frac{45}{25} )^{2} }$

Minimum separation = $\sqrt{(\frac{12}{5} )^{2} +(\frac{9}{5} )^{2} }$ = $\sqrt{\frac{144+81}{25} }$ = $\frac{15}{5}$ = 3

Minimum separation between car and scooter is 3 km

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