# Thread: what is the boat velocity as he jumps on it

1. ## what is the boat velocity as he jumps on it

Batman (mass = 101 kg) jumps straight down from a bridge into a boat (mass = 500 kg) in which a criminal is fleeing.

The velocity of the boat is initially +14 m/s. What is the velocity of the boat after Batman lands in it?
in m/s

not sure about how many dimensions we are working with, and if there are two, then whats really going on, and why its different than one.

So in other words, what makes it two? thanks alot.

2. Originally Posted by rcmango
Batman (mass = 101 kg) jumps straight down from a bridge into a boat (mass = 500 kg) in which a criminal is fleeing.

The velocity of the boat is initially +14 m/s. What is the velocity of the boat after Batman lands in it?
in m/s

not sure about how many dimensions we are working with, and if there are two, then whats really going on, and why its different than one.

So in other words, what makes it two? thanks alot.
Momentum is a vector and is thus conserved in both the vertical and horizontal directions.

Vertically speaking, the boat is going to bob a bit when the Batman lands in it. We don't care about that.

Horizontally speaking we essentially have mass moving with an initial velocity. We are going to add a mass to the boat that has no horizontal velocity. So the situation looks like
$\displaystyle P_{0, tot} = P_{tot}$

$\displaystyle m_{boat}v_{0, boat} = (m_{boat} + m_{Batman} )v$

or
$\displaystyle v = \frac{m_{boat}}{m_{boat} + m_{Batman}} \cdot v_{0, boat}$

-Dan
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