- #1

- 247

- 2

In part 1, a car, m=10^3 kg, is traveling at 28 m/s on a horizontal straight road. The driver sees a tree 100 m away, and with a reaction time of .75 seconds, applies the brakes and stops 9 m short of the tree. What is the decelerating force?

This was not hard, I got -5600 N for the force. F/mg = 4/7, which is important later.

Part b is the part I can't seem to solve. I think I have it right, but it doesn't agree with the answer in the book.

B) Same situation as before, same decelerating force as before, but this time it is on a grade of arcsin (1/10). What speed does the car hit the tree?

For the sum of the X forces, I get f_grav - f_fric = f_car, or since F_fric/mg = 4/7,

mg sin A - (4/7)mg cos A = ma

980 - 5600 cos A = 10^3 a, or a = 4.59

I use v^2 = 28^2 - 2(4.59))(79), and get v^2 = 58.78.

(79 m is the distance to the tree, after subtracting the reaction time distance of D = 28 m/s (.75) = 21 from the total distance of 100 m.)

This all seems right to me, but Mr. French gives the value of v^2 as 42.

Could someone point out where I have gone wrong? (This is not homework, I am using the French text for extra reading and problems.)

Thank you,

Dot