Question

Sam, whose mass is 75 kg , takes off across level snow on his jet-powered skis. The skis have a thrust of 160 N and a coefficient of kinetic friction on snow of 0.1. Unfortunately, the skis run out of fuel after only 15 s .A: What is Sam's top speed?- I found the answer to be 17 m/s (can you check this for me?)B: How far has Sam traveled when he finally coasts to a stop? (I have no idea for this one)

Answer 1

Answer:17.3 m/s

B)282.1 m

Explanation:

First you must be able to determine the normal force in order determine the frictional force. Normal force will be equal and opposite the force of gravity. Force of gravity is equal to mass times the acceleration due to gravity. Therefore the normal force is equal to 75 kg *9.8m/s^2 = 735 N. The frictional force is then the coefficient times the normal force; 0.1*735 so your frictional force is equal to 73.5 N. The net force acting initially will be the thrust- friction because friction always opposes motion. Net force = 160N-73.5N=86.5N. Now using Newtons second law Force = mass * acceleration we can determine the acceleration of the object. 86.5=75kg*a.

This gives you an acceleration of 1.15 m/s^2. Now to determine the max speed, that will be the speed right when the thrust ends. So we use are kinematic equations V(finial)=V(initial)+acceleration*time. With v inital being 0 we get the max speed to be 17.3 seconds.  

Now we can find the distance he traveled in this time using another kinematic formula displacement= V(initial)*time +1/2*acceleration* t^2. We get 129.4 m. However this is just the distance to when the thrusters run out. Now we need to determine to distance to stopping.

Now that the trusters are off the only force slowing him down is friction which we solved for is -73.5 N. Now using newtons second law again we can find the acceleration. -73.5 = 75* acceleration. which is -.98m/s^2.

Now we plug into to find the distance we now at this part we start at a speed of 17.3 and finish ata speed of 0. So using (Vfinal)^2=v(initial)^2+2*acceleration*displacement we find we travelled 152.7 m.

Now add the two distances up to get 282.1 m