Question

1a. Brad (mass 75.0 kg) and Janet (mass 60.0 kg) are doing a pairs figure skating routine on ice. Brad is moving at 5.63 m/s to the east, and Janet is moving at 7.20 m/s to the north. The two skaters meet up and join hands, skating together afterward. What is the pair's velocity after they join hands?

b. A bumper car of mass 125 kg, moving at 6.30 m/s to the north, collides head-on with a second bumper car of mass 100 kg moving at 3.50 m/s to the south. What are the velocities of the first and second bumper cars respectively?

Answer 1

here,

1)

the mass of Brad , m1 = 75 kg

the mass of Janet , m2 = 60 kg

initial velocity of Brad , u1 = 5.63 i m/s

the initial velocity of Janet , u2 = 7.2 j m/s

let the final velocity of combination be v

using conservation of momentum

m1 * u1 + m2 * u2 = (m1 + m2) * v

75 * 5.63 i + 60 * 7.2 j = (75 + 60) * v

v = (3.13 i m/s + 3.2 j m/s)

the magnitude of final velocity |v| = sqrt(3.13^2 + 3.2^2) = 4.48 m/s

the direction of final velocity , theta = arctan(3.2/3.13 ) = 45.6 degree North of East