Calculating Sam's Jet Ski Coasting Distance and Top Speed

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Sam's jet-powered skis generate a thrust of 200N, while the kinetic friction on snow is calculated to be 73.5N, resulting in a net force of 126.5N. This net force leads to an acceleration of 1.69 m/s², allowing Sam to reach a top speed of 16.9 m/s after 10 seconds. To determine how far he coasts after running out of fuel, the deceleration due to friction must be calculated, as it will act as the retarding force. The discussion also touches on a separate problem involving a paratrooper landing in snow, seeking to find the minimum snow depth for safe landing and the impulse experienced. Assistance is requested for both problems, emphasizing the need for detailed calculations.
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Homework Statement


Sam, whose mass is 75 kg, takes off across level snow on his jet-powered skis. The skis have a thrust of 200N and a coefficient of kinetic friction on snow of 0.10. Unfortunately, the skis run out of fuel after only 10 s.

a. What is Sam’s top speed?
b. How far has Sam traveled when he finally coasts to a stop?

Homework Equations





The Attempt at a Solution



Fnet = F(thrust) - Fk
where Fk = (coeff)mg
= (0.1)(75)(9.8)
= 73.5N
plug into Fnet = F (thrust) - Fk
= 200 - 73.5
= 126.5N

To find acceleration:
Fnet = ma
126.5 = 75 a
a = 126.5/75
a = 1.69 m/s2

To find top speed:
Vf = Vi + a (deltaT)
Vf = 0 + 1.69(10)
= 16.9m/s

to find b... i have no idea.
i knwo that:
vi would be 16.9m/s
vf would be 0m/s
i don't know what the decelleration value is for when it is coasting
and i knwo that i use the equation: Vf^2 = Vi^2 + 2a (deltaX)
wehre delta (X) is change in position (displacment)

someone help!
 
Last edited:
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Now the frictional force is the retarding force. From that find the decelleration.
 
In February 1955, a paratrooper fell 370 m from an airplane without being able to open his chute but happened to land in snow, suffering only minor injuries. Assume that his speed at impact was 58 m/s (terminal speed), that his mass (including gear) was 85 kg, and that the force on him from the snow was at the survivable limit of 1.2 105 N.

(a) What is the minimum depth of snow that would have stopped him safely?

?m

(b) What is the magnitude of the impulse on him from the snow?


? kg·m/s

PLEASE HELP ON THIS PROBLEM
ANY HELP ON THIS PROBLEM WILL BE GREATLY APPRECIATED
 
Show some work in the second problem
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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