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How fast would you have to throw a 150-g rock for it to have the same momentum as a 10-g sniper rifle bullet traveling at 900 m/s?
A
60 m/s
B
400 m/s
C
40 m/s
D
600 m/s
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1
First, understand that momentum (p) is given by the formula: , where is mass and is velocity.
Calculate the momentum of the bullet. Use the given mass of the bullet, 10 g (which is 0.01 kg in SI units), and its velocity, 900 m/s. Substitute these values into the momentum formula: .
Set the momentum of the rock equal to the momentum of the bullet. Let the velocity of the rock be . The mass of the rock is 150 g (which is 0.15 kg in SI units). So, the equation becomes: .
Solve for the velocity of the rock, , by dividing both sides of the equation by 0.15: .
Evaluate the expression to find the velocity of the rock. This will give you the speed at which the rock must be thrown to have the same momentum as the bullet.