A large cannon, which is attached to a railroad car, shoots a 15 kg projectile w

Question

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?

Please give a thorough explanation for all work. Physics is a difficult subject for me and for me to succeed in this class I really need to understand how you arrived at each answer – thanks!

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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