Batman (mass = 94 kg) jumps straight down from a bridge into a boat (mass = 540

Question

Batman (mass = 94 kg) jumps straight down from a bridge into a boat (mass = 540 kg) in which a criminal is fleeing. The velocity of the boat is initially + 17 m/s. What is the velocity of the boat after Batman lands in it? m/s The drawing shows a collision between two pucks on an air-hockey table. Puck A has a mass of 0 024 kg and is moving along the x axis with a velocity of + 5.5 m/s. It makes a collision with puck B, which has a mass of 0.059 kg and is initially at rest. The collision is not head-on. After the collision, the two pucks fly apart with the angles shown in the drawing. (a) Find the final speed of puck A. m/s (b) Find the final speed of puck B. m/s

Explanation / Answer

a)

let

m1 = 0.024 kg, u1 = 5.5 m/s

m2 = 0.059 kg

let v1 and v2 are the final speeds of puck A and puck B.

Apply conservation of momentum in y-direction

0 = m1*v1*sin(65) - m2*v2*sin(37)

v2 = (m1*sin(65)/m2*sin(37))*v1

= (0.024*sin(65)/(0.059*sin(37))*v1

v2 = 0.6126*v1

now apply conservation of momentum in x-direction

m1*u1 = m1*v1*cos(65) + m2*v2*cos(37)

0.024*5.5 = 0.024*v1*cos(65) + 0.059*0.6126*v1*cos(37)

==> v1 = 3.38 m/s <<<<<<<<-------------Answer

b) v2 = 0.6126*v1

= 0.6126*3.38

= 2.07 m/s <<<<<<<<-------------Answer

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