Problem 3 (12 points): An evil villain shoots a rapid-fire rail gun at Superman.

Question

Problem 3 (12 points): An evil villain shoots a rapid-fire rail gun at Superman. The gun fires 1.00-kg projectiles at a rate of 10 per second and at a speed of 500. m/s. As the projectiles strike Superman he leals forward so that they deflect straight down (thus avoiding ricochets hitting innocent bystanders). Superman has a mass of 100. kg. a) What is the speed of the projectiles after colliding elastically with Superman? b) Find the average force (magnitude and direction) of the deflected projectiles acting on Superman.

Explanation / Answer

given

mass of projectiles, m = 1 kg

rate = r = 10 projectiels per second

spee do fprojectiles, v = 500 m/s

a. as the projectiles collide elastically with the superman, their speed remain unchanged

hence speed after elstically colliding with the superman, speed of projectiels is v = 500 m/s

b. initial momentum if projectile = mv i ( in i direction)

final momentum of projectile = mv j ( in j direction)

hence change in momentum = mv(j - i)

hence

average force = rate of change of moemntum = 10mv(j - 1) = 5000(j - i)

hence magnitude of net force on superman = sqroot(1 + 1)5000 = 7071.06781 N

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