Jason takes off across level water on his jet-powered skis. The combined mass of Jason and skis is 75 kg (the mass of the fuel is negligible). The skis have a thrust of 200 N and a coefficient of kinetic friction on water of 0.1. Unfortunately, the skis run out of fuel after only 11 s. How far has Jason traveled when he finally coasts to a stop?
A. 24 m/s
B. 90 m/s
C.150 m/s
D.240 m/s
And help find acceleration? Please help
1 Answer
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newton’s second law tells us
sum of forces = ma
while he has fuel, this becomes
thurst – friction = ma
thrust = 200N, friction = u mg = 0.1*75kg*938m/s/s
thus,
200N – 73.5N = 75 a
a=1.69m/s/s
in the first 11 seconds, Jason reaches a velocity of
v= a t = 1.69m/s/s x 11 s = 18.6m/s
and travels a distance dist = 1/2 a t^2 = 1/2(1.69m/s/s)(11s)^2 = 102.2m
once he runs out of fuel, the only force acting on him is friction, so his acceleration then is
F = ma = u mg or a = u g = 0.98m/s/s
and we find the distance he travels while coasting from
vf^2=v0^2+ 2ad
vf=final velocity =0
v0=initial velocity = 18.6m/s
a=accel = -0.98m/s/s
d=distance traveled
0=18.6^2-2*0.98*d => d=176.5m
add the two distances to find his total distance traveled
