Determining impulse given stopping distance and change in velocity

[I_Try_Math]

Homework Statement

A car crashes into a large tree that does not
move. The car goes from 30 m/s to 0 in 1.3 m.
(a) What impulse is applied to the driver by the
seatbelt, assuming he follows the same motion
as the car? (b) What is the average force applied
to the driver by the seatbelt?

Relevant Equations

$j = \int F(t) dt$
$\Delta KE=W=F*distance$

I think I was able to work out that $F=-346.2m$ and that $t= .087 sec$ but maybe I'm wrong. Without knowing the mass, I'm not sure how I can find the impulse.

Any hints or corrections are appreciated.

 

[haruspex]

Without knowing the mass, I'm not sure how I can find the impulse.

You can't. Just set the mass as "m" and write an expression using that.

The other problem with the question is that even if you knew the mass you would still not be able to work out the average force.
As you wrote, average force is defined as momentum change divided by elapsed time, but you do not know the time. If you calculate it as energy change divided by distance you will in general get a different answer (the "force averaged by distance"). The answers are the same if the force is constant, but if that is to be assumed there is no need to ask for an average.
http://hyperphysics.phy-astr.gsu.edu/hbase/impulse.html#c2b

A constant force would be the ideal, but in practice some distance will be covered while it rises to a peak.

 

[kuruman]

Your answers are correct under the assumption that the acceleration is constant and the best you can do if you are not given the mass of the person and the time interval over which the car stops.

Considering that the average car is about 5 m long and that the tree doesn't move, the car is reduced to about 3/4 of its original length. That does not bode well for the driver, seat belt or no seat belt.

 

[I_Try_Math]

You can't. Just set the mass as "m" and write an expression using that.

The other problem with the question is that even if you knew the mass you would still not be able to work out the average force.
As you wrote, average force is defined as momentum change divided by elapsed time, but you do not know the time. If you calculate it as energy change divided by distance you will in general get a different answer (the "force averaged by distance"). The answers are the same if the force is constant, but if that is to be assumed there is no need to ask for an average.
http://hyperphysics.phy-astr.gsu.edu/hbase/impulse.html#c2b

A constant force would be the ideal, but in practice some distance will be covered while it rises to a peak.

The textbook has a similar word problem a couple questions before this where the mass of a car is given. I believe the authors intended to indicate that the same mass should be used for this question but forgot.

Anyway thank you for your explanation, I wanted to make sure I wasn't missing a possible way to solve it.

 

[haruspex]

The textbook has a similar word problem a couple questions before this where the mass of a car is given. I believe the authors intended to indicate that the same mass should be used for this question but forgot.

The mass of the driver is unlikely to equal the mass of the car.

 

[I_Try_Math]

The mass of the driver is unlikely to equal the mass of the car.

Oh right, I got confused as to what the question was asking for. I just looked it up to double check and the answer the textbook gives is $-2,100 kg \cdot m/s$ which doesn't appear to make sense based off the given information in the question, as you said. Not exactly sure how it happened but it's some kind of typo or mistake in the answer key for sure.

 

[Mister T]

Evidently the driver has a mass of 70 kg. The author left that out by mistake.