1. (24 points) A large cannon, which is attached to a railroad car, shoots a 15

Question

1. (24 points) A large cannon, which is attached to a railroad car, shoots a 15 kg projectile with
a muzzle velocity of 250 m/s. The railroad car and the cannon have a total mass of 1500 kg.
It is sitting at the edge of a cliff that is h1 = 350 m above the bottom of a large canyon. A
target is located on the on the opposite side of
the canyon, which is h2 = 470 m above the
bottom of the canyon.
a. If the cannon, while pointed at an angle
of 30° above the horizontal, fires a
projectile and hits the target, what is the
horizontal distance to the target?
b. If the railroad car is not anchored down and is free to move on its tracks, what is the
magnitude and direction (toward or away from the cliff edge) of the railroad car’s
velocity just after it fires the projectile?

Explanation / Answer

a) t= (470-350)/250sin30=0.96 sec (time taken to hit the target) horizontal distance= 250cos30x0.96=207.85m (in this time horizontal component of velocityxtime=horizontal distance) b) from momentum conservation the rail road move in horizontal direction opposite to that of the velocity of projectile i.e in backward direction (1500-150)v-150x250=0 (before firing momentum was zero after it should be zero) v=27.78m/s

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