Question

Batman (mass = 88.6 kg) jumps straight down from a bridge into a boat (mass = 484 kg) in which a criminal is fleeing. The velocity of the boat is initially +8.25 m/s. What is the velocity of the boat after Batman lands in it?

Answer 1

The velocity of the boat after Batman lands in it is 6.97 m/s.

Step-by-step explanation:

Given that,

Mass of batman, m = 88.6 kg

Mass of boat, m' = 484 kg

The velocity of the boat is initially +8.25 m/s, v' = 8.25 m/s

We need to find the velocity of the boat after Batman lands in it. In this case, the conservation of linear momentum works. So,

Initial momentum = final momentum

`mv+m'v'=(m+m')V`

v = 0 (as the batman was at rest initially)

`m'v'=(m+m')V\\\\V=(m'v')/((m+m'))\\\\V=(484* 8.25)/((88.6+484))\\\\V=6.97\ m/s`

So, the velocity of the boat after Batman lands in it is 6.97 m/s.