Two dogs, Rover and Fido, run on a level frictionless surface. Rover runs eastward with a momentum of $24 \mathrm {~kg} \cdot \mathrm { m } / \mathrm { s }$ and Fido runs northward with momentum $10 \mathrm {~kg} , \mathrm {~m} / \mathrm { s }$ They make a sudden perfectly inelastic collision. What is the magnitude of their combined momentum after the collision?
A) $34 \mathrm {~kg} \cdot \mathrm { m } / \mathrm { s }$
B) $26 \mathrm {~kg} \cdot \mathrm { m } / \mathrm { s }$
C) $14 \mathrm {~kg} \cdot \mathrm { m } / \mathrm { s }$
D) It cannot be determined without knowing the masses and velocities of the dogs.

Question

Quizplus · Accepted Answer

The momentum of the system before the collision is conserved after the collision. Since momentum is a vector quantity, we calculate the resultant momentum using the Pythagorean theorem: $\sqrt{24^2 + 10^2} = \sqrt{576 + 100} = \sqrt{676} = 26 \mathrm {~kg} \cdot \mathrm { m } / \mathrm { s }$.

Two Dogs, Rover and Fido, Run on a Level Frictionless 24 kg⋅m/s24 \mathrm {~kg} \cdot \mathrm { m } / \mathrm { s }24 kg⋅m/s

Two Dogs, Rover and Fido, Run on a Level Frictionless $24 \mathrm {~kg} \cdot \mathrm { m } / \mathrm { s }$