What Is Sam's Top Speed and Travel Distance on Jet Powered Skis?

In summary, Sam, who weighs 80 kg, is skiing on jet powered skis with 189N thrust and a coefficient of kinetic friction of 0.1 on snow. After 12 seconds, the skis run out of fuel. Part A asks for Sam's top speed, which can be found using the equation F-uk(n) = m(Ax) and acceleration = velocity/time. The correct answer is 16.578 m/s. For part B, the change in displacement can be found using the equation Vxf^2 = Vxi^2 + 2(Ax)(delta x), but the wrong answer of 198.936m was obtained. Another approach is to use the fact that frictional force
  • #1
aligass2004
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Homework Statement



Sam, whose mass is 80 kg, takes off across level snow in his jet powered skis. The skis have a thrust of 189N and a coefficient of kinetic friction on snow of 0.1. Unfortunately, the skis run out of fuel after only 12s. a.) What is Sam's top speed? b.) How far has Sam traveled when he finally coasts to a stop?

Homework Equations



Fk = uk(n)
F=ma

The Attempt at a Solution


I solved part A by using F-uk(n) = m(Ax). I solved for Ax, and got the answer to be 1.3815. I then used acceleration = velocity/time to find the velocity. I got the velocity to be 16.578, which is right. For part B I tried using Vxf^2 = Vxi^2 + 2(Ax)(delta x) to find the change in displacement. I got 198.936m, which was wrong.
 
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  • #2
For the second part use the fact that
Frictional_force x distance = work_done_to_stop_skier = kinetic_energy_of_skier.
 
  • #3


I would like to point out that the calculated top speed of 16.578 m/s is only an approximation as it assumes constant acceleration, which may not be the case in this scenario. Additionally, the coefficient of kinetic friction may vary depending on the conditions of the snow, which could affect the accuracy of the calculations. Furthermore, the use of jet powered skis on snow may have safety implications and it is important for individuals to use caution and follow proper safety protocols when engaging in such activities. As for part B, the equation used (Vxf^2 = Vxi^2 + 2(Ax)(delta x)) may not be applicable in this scenario as it assumes constant acceleration and does not take into account the decrease in velocity due to the skis running out of fuel. Further calculations or assumptions would be needed to accurately determine the distance traveled by Sam before coming to a stop.
 

FAQ: What Is Sam's Top Speed and Travel Distance on Jet Powered Skis?

1. What is the difference between top speed and displacement?

Top speed refers to the maximum speed that an object can achieve, while displacement refers to the distance an object has moved from its original position.

2. How is top speed measured?

Top speed is typically measured in units of speed, such as miles per hour (mph) or kilometers per hour (km/h). It can also be measured in terms of meters per second (m/s) or feet per second (ft/s).

3. What factors affect an object's top speed?

The top speed of an object can be affected by various factors, including the object's weight, aerodynamics, engine power, and road conditions. In general, a lighter and more streamlined object with a powerful engine will have a higher top speed.

4. Can an object's displacement affect its top speed?

Yes, an object's displacement can affect its top speed. In general, the greater the displacement, the longer it will take for the object to reach its top speed. This is because the object has to overcome a greater distance to accelerate to its maximum speed.

5. Is there a limit to how fast an object can go?

According to Einstein's theory of relativity, there is a speed limit in the universe known as the speed of light, which is approximately 299,792,458 meters per second. This means that no object can travel faster than the speed of light in a vacuum. However, for everyday objects, there is no practical limit to their top speed.

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