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Q.

A gun kept on a straight horizontal road, is used to hit a car travelling along the same  road away from the gun. With a uniform speed of  72km/hr. The car is at a distance of 500m from the gun when the guns fired at an angle of  450 with the horizontal. The  distance of the car from the gun when the shell hits the car is _____m. (g=9.8m/s2)

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answer is 747.

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Detailed Solution

The shell hits the car after a time T sec
At a distance ‘R’ from the gun.
 Question Image

R=u2sin2θg=u2sin900g=u2g
Time of flight,  T=2usin450g=2ug
According to problem 
R=500+VT        V=72×518=20           u2g=500+20(2ug)          u2202u500g=0             u2202u500×9.8=0        u=10[2±51]       Taking +ve sign        u=10[2+51]=85.56m/s       Distance,  R=u2g=(85.56)29.8  =747m

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