Question

Two students of masses m1 = 60Kg, m2 = 75Kg are passing each other a ball of mass m = 1.5kg. They are on skates on frictionless ice. The first student passes the ball to the second one throwing it at a velocity v1 = 25m/s at an angle 30? . The second one throws it back at the first one at a velocity v2 = 25m/s at an angle 45? . After the first student received the ball back, what are the velocities of the two students? And how much mechanical energy has been lost in this whole game?

Answer 1

for the first student :

while throwing the ball :

consider the momentum along the horizontal direction

P_i = initial total momentum of ball and student = 0 (since ball and student were at rest)

P_f = momentum of ball + momentum of student after throw = m₁ v₁ Cos30 - m_b v_b

using conservation of momentum

P_f = P_i

m v₁ Cos30 - m₁ v = 0

(1.5) (25) Cos30 - (60) v = 0

v = 0.54 m/s

while receving the ball :

momentum before catching = momentum after catching

m₁ v + m v₂ Cos45 = (m₁ + m) V

(60) (0.54) + (1.5) (25) Cos45 = (60 + 1.5) V

V = 0.96 m/s

for the second student :

while catching

initial momentum before catching = final momentum after catching

m v₁ Cos30 = (m + m₂) V'

(1.5) (25) Cos30 = (1.5 + 75) V'

V' = 0.425 m/s

while throwing :

momentum before throwing = momentum after throwing

(1.5 + 75) V' = - m v₂ Cos45 + m₂ V''

(1.5 + 75) (0.425) = - (1.5 x 25) Cos45 + (75) V''

V'' = 0.787 m/s