Kinematics, Newton's Laws, Fun With Engineers

tri5

1. The problem statement, all variables and given/known data

As a prank, your friends have kidnapped you in your sleep, and transported you out onto the ice covering a local pond. Since you're an engineer, the first thing you do when you wake up is drill a small hole in the ice and estimate the ice to be 6.7cm thick and the distance to the closest shore to be 29.4 m. The ice is so slippery (i.e. frictionless) that you cannot seem to get yourself moving. You realize that you can use Newton's third law to your advantage, and choose to throw the heaviest thing you have, one boot, in order to get yourself moving. Take your weight to be 545.0 N. (Lucky for you that, as an engineer, you sleep with your knife in your pocket and your boots on.)

1) (a) What direction should you throw your boot so that you will most quickly reach the shore?
away from the closest shore

2) (b) If you throw your 1.11-kg boot with an average force of 416.0 N, and the throw takes 0.632 s (the time interval over which you apply the force), what is the magnitude of the force that the boot exerts on you? (Assume constant acceleration.)
416 N

3) (c) How long does it take you to reach shore, including the short time in which you were throwing the boot?


2. Relevant equations

v = v_0 + a t
x = x_0 + v_0 t + (1/2) a t^2
v^2 = v_0^2 + 2 a \Delta x
\vec{F}_{net} = \Sigma \vec{F} = m \vec{a}

3. The attempt at a solution
I am having trouble with question 3 of this problem. I calculated the acceleration using 416 N and the mass minus the boot. I then use x = x_0 + v_0 t + (1/2) a t^2
to calculate time. The automated homework system says the answer is wrong.

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Dick

You are not moving at a constant acceleration the whole distance to shore. The acceleration is only constant while you are throwing the boot. After that your velocity is constant.

tri5

Well I tried what you said doing constant velocity but the automated homework system says the answer is still wrong.

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runningninja

Have you tried using momentum and impulse?

tri5

In class we have only covered 1d, 2d kinematics, and Newton's laws. I know momentum is just a restatement of Newtons's 2nd law, but it has not been covered in class yet. The professor insists that this problem can be solved correctly using what was taught in class so far.

D H

You will cover some distance on the ice between the time that you start the throw and the time you let go of the boot. You did not account for this in your answer.

In other words, you shouldn't be using 29.4 meters the way you did in your work.

Dick

Now you are taking the whole distance travelled at a constant velocity. That's not right either. He travels part of the way while accelerating and part of it at constant velocity. It's not really clear to me that they mean you to subtract the mass of the boot either.

D H

I agree. That "Take your weight to be 545.0 N." is a bit ambiguous. However, the parenthetical remark "(Lucky for you that, as an engineer, you sleep with your knife in your pocket and your boots on)" suggests that that 545.0 newtons includes the knife and the boots.


Aside: This is a *bad* question. I calculate that the engineer's throwing arm has to be over 90 meters long.

Dick

Good point. I guess an engineer should be expected to carry an extension throwing arm as well.