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Question

A cannon ball of mass 2 kg is fired at a target 500 m away. The 400 kg cannon recoils with a velocity of 2 ms−1. Assuming cannon ball moves with constant velocity, when does it hit the target?

A

5 sec

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B

10 sec

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C

15 sec

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D

2 sec

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Solution

The correct option is A

5 sec


Given: mass of cannon, m1=400 kg, mass of cannonball, m2=2 kg, cannon recoil velocity, v1=2 ms1 (The negative sign indicates that the recoil velocity is opposite to the direction of cannon velocity.), target distance s=500 m
Let the speed of the cannonball be v2. Let the time taken to hit the target be t.

Total initial momentum =0 (as both the cannon and the cannonball are at rest)
Total final momentum =m1v1+m2v2

From the law of conservation of momentum,
Total momentum before firing = Total momentum after firing
0=m1v1+m2v2

0=(400×(2))+(2×v2)

v2=400×22=400 ms1
Hence, the velocity of the cannonball is 400ms1.

Time t=sv2=500400=1.25 s
Thus, the time taken to hit the target=1.25 s.

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