Anthony and Sissy are participating in the "Roll-a-Rama" rollerskating dance championship. While 75.6 kg Anthony rollerskates backwards at 3.7 m/s, 59 kg Sissy jumps into his arms with a velocity of 5.4 m/s in the same direction. How fast does the pair roll backwards together? Answer to the nearest tenth of a m/s.

4.4 m/s

Explanation:

momentum is always conserved so we can use conversation of momentum to solve the question, also momentum is a vector quantity (it has magnitude and direction) which is the product of the bodies mass and velocity.

conservation law of momentum relates by the formula below:

momentum before collision = momentum after collision

M1U1 + M2U2 = M1V1 + M2V2

in the case of this two, the formula becomes

M1U1 + M2U2 = V (M1 + M2) since she jumped into his arm

there masses are M1 = 75.6 kg M2 = 59 kg and their velocities are U1 = 3.7 m/s and U2 = 5.4 m/s, their common velocity after collision = V since their motion is backward the formula becomes

-M1U1 - M2U2 = V (M1 + M2)

substitute the values into the equations

(-75.6 * 3.7) + ( - 59 * 5.4) = V (75.6 + 59)

- 598.32 = 134.6 V

divide both side by 134.6

V = - 598.32 / 134.6 = - 4.445 m/s = - 4.4 m/s to nearest tenth the negative means in the same backward direction