recoil velocity problem?

Question

One of James Bond's adversaries is standing on a frozen lake; there is no friction between his feet and the ice. He throws his steel-lined hat with a velocity of v at an angle theta above the horizontal, hoping to hit James.

If his mass is m1 and that of his hat is m2, what is the magnitude of his horizontal recoil velocity?

Thanks for the help!

Answer 1

Conservation of momentum gives

m1 * voddjob = m2 * vcostheta solve for voddjob

Answer 2

this is a conservation of momentum problem.

m1v + m2v(recoil) must be the same before and after the throw.

m1v + m2v(recoil) before the throw = 0, (both velocities are 0 before the throw) so it must = 0 AFTER the throw, too!

the horizontal component of the hat velocity is (v) x (cos theta)

(if theta is zero and the hat is thrown horizontally, the cos = 1 and ALL of the horizontal component = v)

so (m1)(v of hat)(cos theta) + (m2)(v recoil) =0

v recoil = - (m1)(v of hat)(cos theta) / (m2)

now, see if it makes sense....

yes the velocity of recoil WOULD be in the opposite direction, hence the minus sign, and

if the man's mass, m2, were very very large, the recoil velocity would be small. (also if the hat's mass is very, very small)

YAY it all makes sense!

Answer 3

this could be a conservation of momentum project. m1v + m2v(turn away) ought to choose to be an same previously and after the throw. m1v + m2v(turn away) previously the throw = 0, (the two velocities are 0 previously the throw) so it ought to choose to = 0 AFTER the throw, too! the horizontal element of the hat velocity is (v) x (cos theta) (if theta is 0 and the hat is thrown horizontally, the cos = a million and each and all of the horizontal element = v) so (m1)(v of hat)(cos theta) + (m2)(v turn away) =0 v turn away = - (m1)(v of hat)(cos theta) / (m2) now, see no count form if it particularly is wise.... specific the fee of turn away must be indoors the alternative direction, hence the minus sign, and if the guy's mass, m2, have been very very super, the turn away velocity must be small. (additionally if the hat's mass is very, very small) YAY all of it somewhat is wise!