# A canoe in a still lake is floating North at #8 m/s#. An object with a mass of #20 kg# is thrown North East at #3 m/s#. If the mass of the canoe was #200 kg # before the object was thrown, what is the new speed and direction of the canoe?

##### 2 Answers

See principle below I leave the final math to you.

#### Explanation:

Work this out as a momentum problem.

Momentum =

Momentum of canoe =

Momentum of rock =

Resolve momentum vector of rock into north and east component:

North component:

East component :

So combined canoe + rock momentum is two vectors:

North:

East :

Resultant vector magnitude is:

Direction:

The new speed is 7.79 m/s and the direction is

#### Explanation:

Momentum is conserved.

Momentum before = momentum after

The previous equation and the following equation is the statement of conservation of momentum in this case.

where

The statement of the problem allow 2 different interpretations. When it says that the object was thrown North East at 3 m/s, was the 3 m/s with respect to the canoe or to the lake? If with respect to the lake is what was meant, since the canoe's velocity was 8 m/s, the object was actually thrown South East

The momentum equation needs to be done separately for the North direction and the East direction.

**North:**

Entering the data, the momentum equation becomes

Solving for

**East:**

Entering the data, the momentum equation becomes

Solving for

So this component of the final velocity is actually west.

The new speed is the vector sum of

I hope this helps,

Steve