Can a skidding car stop in 50 ft on a 20° incline?

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Homework Statement



While visiting a friend in San Francisco, you decide to drive around the city. You turn a corner and find yourself going up a steep hill. Suddenly a small boy runs out on the street chasing a ball. You slam on the brakes and skid to a stop, leaving a skid mark 50 ft long on the street. The boy calmly walks away, but a policeman watching from the sidewalk comes over and gives you a ticket for speeding. You are still shaking from the experience when he points out that the speed limit on this street is 25 mph.
After you recover your wits, you examine the situation more closely. You determine that the street makes an angle of 20° with the horizontal and that the coefficient of static friction between your tires and the street is 0.80. You also find that the coefficient of kinetic friction between your tires and the street is 0.60. Your car's information book tells you that the mass of your car is 1570 kg. You weigh 130 lb, and a witness tells you that the boy had a weight of about 60 lbs and took 3.0 s to cross the 15-ft wide street. Will you fight the ticket in court?

Homework Equations





The Attempt at a Solution



i got x: Ffriction + Fx

=

0.6mgCos(theta)+mosin(theta)
 
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Discussion

Doing exam questions are a little dubious on the homework forum.

Besides you've shown no real effort.
 
Alright this an old exam question. Here is my progress :

use the equation v^2-v0^2 = 2x(x-x0)

by trig I figured out,

Fnet = F of friction + F of x direction

= 0.6mgCos(@)+mgSin(@)

so,

v^2 = 0, Vo^2 = ? ,

a = Fnet/m
=

g(0.6Cos(theta) +gsin(theta)).

so

Vo^2 = 2F/m(X-Xo)

= sqrt ( 2 (g(.6Cos(@) + sin(@))(15.14)

= 16.44m/s
 
that translates to 36mph. I am not sure if my logic is correct though, which
is why i wanted someone to check it.

IF this is correct then he is guilty.
 
tnutty said:
that translates to 36mph. I am not sure if my logic is correct though, which
is why i wanted someone to check it.

IF this is correct then he is guilty.

Yep. He should just mail in the fine and wait for his auto insurance rates to go up.