Forensic scientists can measure the muzzle velocity of a gun by firing a bullet

Question

Forensic scientists can measure the muzzle velocity of a gun by firing a bullet horizontally into a large hanging block that absorbs the bullet and swings upward. (See the figure below.) The measured maximum angle of swing can be used to calculate the speed of the bullet. In one such test, a rifle fired a 4.20g bullet into a 2.50kg block hanging by a thin wire 75.0cm long, causing the block to swing upward to a maximum angle of 30.2° from the vertical.

What was the original speed of this bullet?

v=_____________m/s2

Explanation / Answer

When something swings up, it goes sideways some and up some. If we take cos(30.2) we will be able to find how far down it is from the ceiling at its highest point. 0.75m*cos(30.2) = 0.648m down from ceiling It started out 0.75m down from the ceiling, so it went up 0.75m - 0.648m = 0.102m The sideways component takes no work since gravity is down. Kinetic energy of the block plus bullet is converted to gravitational potential energy. m = mass bullet M = mass block v = pre-collision speed bullet V = post collision speed of block (1/2)(M + m)V^2 = (M + m)g*h V^2 = 2*g*h V = SQRT(2gh) = SQRT(2*9.8*0.102)m/s = 1.41 m/s Momentum is conserved mv = (M + m)V v = (M + m)V/m = 2.5042kg*1.41m/s/0.0042kg = 842 m/s this is the bullet speed Note units are m/s; not m/s^2 Further note 'm' isn't such a good variable, since we used meters in our units.

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