The speeds of a tortoise and a hare are `2 ms^(-1)` and `5 ms^(-1)`, respectively. The mass of the hare is 3 kg and that of the tortoise is 10 kg. Which of the two has greater momentum? (Assume speed of each to be steady.)

Explanation

We have seen above that, momentum = `"mass"xx"velocity"`
Velocity being a vector quantity has both magnitude and direction. In the question, only the magnitude of velocity, i.e., speed, is given. There is no information regarding the direction of motion of the hare and the tortoise. Since it is not possible to compare two vectors, it is not possible to compare their momenta. However, we can compare the magnitudes of their momenta as below.
Mass of tortoise = 10 kg.
Speed of tortoise = 2 m `s^(-1)`
`P_("tortoise") = 10 xx 2 = 20 kg m s^(-1)`
Mass of the hare = 3 kg
Speed of the hare = 5 m `s^(-1)`
`P_("hare") = 3 xx 5 = 15 kg m s^(-1)`
Thus, the magnitude of momentum of the tortoise is greater than that of the hare.