Calculating final speed using momentum

[ilovedeathcab]

calculating final speed using momentum [solved]

1. A 73.8 kg girl runs at 4 m/s and jumps onto a 3.4 kg stationary skateboard. Ignore friction and calculate the final speed of the girl.

* DO NOT include units in your answer.
* Give your answer with one decimal.
* Answers will be accepted if they are within 0.2 of the correct answer.
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2. I understood that this uses the law of conservation of momentum, but couldn't get past this basic equation without getting it wrong.
m1v1i + m2v2i = m1v1f + m2v2f

Assuming object 1 is the girl, and object 2 is the skateboard, v2i would equal 0 (stationary skateboard), v1i would equal 4m/s (girl), and you would plug in the masses (m1=73.8, m2=3.4kg). I'm not sure what to put in for v2f, becuse it doesn't specify in the problem the final velocity of the skateboard. I'm pretty sure I'm missing the big picture.

 

[rock.freak667]

The girl and the skateboard move with the same final velocity.

 

[thomate1]

The final speed of the girl can be calculated using the law of conservation of momentum, which states that the total momentum of a system remains constant in the absence of external forces. In this case, the initial momentum of the girl (m1v1i) must equal the final momentum of the girl and skateboard together (m1v1f + m2v2f). Therefore, we can set up the following equation:

m1v1i = m1v1f + m2v2f

Substituting in the given values, we get:

73.8kg * 4m/s = 73.8kg * v1f + 3.4kg * v2f

Rearranging the equation to solve for v1f (the final speed of the girl), we get:

v1f = (73.8kg * 4m/s - 3.4kg * v2f) / 73.8kg

Now, we need to find the final velocity of the skateboard (v2f) in order to solve for v1f. Since the skateboard and girl are now moving together as one system, their final momentum will be equal to the initial momentum of the girl (m1v1i). Therefore, we can set up another equation:

m1v1i = m1v1f + m2v2f

Substituting in the values, we get:

73.8kg * 4m/s = 73.8kg * v1f + 3.4kg * v2f

Since we already know the value of v1f, we can plug that in and solve for v2f:

73.8kg * 4m/s = 73.8kg * ((73.8kg * 4m/s - 3.4kg * v2f) / 73.8kg) + 3.4kg * v2f

Simplifying and solving for v2f, we get:

v2f = 0.98m/s

Now that we have both v1f and v2f, we can plug them back into the original equation to solve for the final speed of the girl:

v1f = (73.8kg * 4m/s - 3.4kg * 0.98m/s) / 73.8kg = 3.95