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Question
A cricket ball of mass 150 g has an initial velocity `u = (3hati + 4hatj)` m s−1 and a final velocity `v = - (3hati + 4hatj)` m s−1 after being hit. The change in momentum (final momentum-initial momentum) is (in kg m s1)
Options
zero
`-(0.45 hati + 0.6 hatj)`
`-(0.9 hati + 1.2 hatj)`
`-5 (hati + hatj)`
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Solution
`-(0.9 hati + 1.2 hatj)`
Explanation:
Given, `u = (3hati + 4hatj)` m/s
And `v = - (3hati + 4hatj)` m/s
Mass of the ball = 150 g = 0.15 kg
Δp = Change in momentum
= Final momentum – Initial momentum
= `mv - mu`
= `m(v - u) = (0.15) [- (3hati + 4hatj) - (3hati + 4hatj)]`
= `(0.15) xx [ - 6hati - 8hatj]`
= `- [0.15 xx 6hati + 0.15 xx 8hatj]`
= `- [0.9 hati + 1.20 hatj]`
Hence, Δp = `-[0.9 hati + 1.2 hatj]`
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