Sam, whose mass is 76kg , takes off across level snow on his jet-powered skis. The skis have a thrust of 220N and a coefficient of kinetic friction on snow of 0.1. Unfortunately, the skis run out of fuel after only 15s .
How far has Sam traveled when he finally coasts to a stop?
Anonymous, imagine responding 3 years later, my home boy Devron been waiting for an answer for 3 years
Ignore the work done.
This is a multistep problem and Fnet doesn't equal 220N.
Fnet=Fthrust-Fk
Fnet=220N-74.48N=145.52N
Solve for acceleration:
F=ma
a=F/m
a=145.52N/76kg
a=1.91m/s^2
Use the following kinematic equation:
d=vi*t+1/2at^2
where
Vi=0m/s
a=1.91m/s^2
t=15s
and
d=?
Solve for d:
d=0 + 1/2(1.91m/s^2)*(15s)2
d=214.8m
Use the following kinematic equation to find the velocity of the skier:
d=Vf*t-1/2at^2
Where
d=214.8m
Vf=?
a=1.91m/s^2
and
t=15s
Solve for Vf:
Vf=[d+1/2at^2]/t
Vf=[214.8m+1/2(1.91m/s^2)(15s)^2]/15s
Vf=28.59m/s
The first leg of the trip, what about the second leg of the trip?
The frictional force will be equal the net force after the fuel has stopped providing a thrust.
1/2mv^2=Fk*d
1/2mv^2=mk*m*g*d
1/2v^2=mk*g*d
Where
v=28.59
mk=0.1
g=9.8m/s^2
and
d=?
Solve for d:
1/2(28.59m/s)^2=(0.1)(9.8m/s^2)*d
408.69=0.98*d
d=417m
d=417m+215m=632m
*** Still not sure that this completely correct, so hopefully someone comes by and double checks this.
Lmao so we all just here for mastering physics huh XD
After the skis run out of fuel, the Force of kinetic friction will do work on the skier.
220N=*d
Solve for d:
220N=m*g*µk*d
220N=(76kg)*(9.8m/s^2)*(0.1)*d
220N=74.48N*d
d=220N/74.48N
d=2.95m=3m
I could be wrong.
correct!
Yep, I sorta did what my name says. I'm also really late to the party
To find the distance Sam traveled when he finally coasts to a stop, we need to calculate the acceleration of Sam first.
The thrust force from the jet-powered skis can be calculated using Newton's second law, which states that the force is equal to the mass multiplied by the acceleration (F = ma). Rearranging the formula, we can calculate the acceleration (a) by dividing the thrust force (F) by the mass (m):
a = F / m
Plugging in the values, we have:
F = 220 N (thrust force)
m = 76 kg (mass of Sam)
a = 220 N / 76 kg
a ≈ 2.89 m/s²
Now that we have the acceleration, we can determine the distance traveled by using the formula for distance covered with constant acceleration:
d = v₀t + 0.5at²
We know that the skis run out of fuel after 15 seconds, so the time (t) is 15 seconds. To find the initial velocity (v₀), we can use the fact that Sam starts from rest, so v₀ = 0.
Plugging in the values, we have:
v₀ = 0 m/s
t = 15 s
a = 2.89 m/s²
d = (0 m/s)(15 s) + 0.5(2.89 m/s²)(15 s)²
d = 0 + 0.5(2.89 m/s²)(225 s²)
d = 0 + 329.175 m
d ≈ 329.175 m
Therefore, Sam has traveled approximately 329.175 meters when he finally coasts to a stop.