Question about Newton's laws, solving for distance given slope and speed.

[avaholic]

1. A car coasts (engine off) up a 30 degree grade. If the speed of the car is 25 m/s at the bottom of the grade, what is the distance traveled before it comes to a rest?



2. mostly my class so far has dealt with equations calculating work and force by drawinf free body diagrams and using the trig functions.



3. I'm having a hard time solving this as I'm missing any sort of mass value, which would seem necessary. i though of using the equation for change in kinetic energy, but can't think of how to rearrange it in a helpful way. The solution in the back of the textbook is 64m, but i can't honestly think of a way to get there.

 

[rl.bhat]

To solve this problem mass is not necessary.
Which force is acting on the car while going up. Which component of this force retards the car? From that you can find the retardation.
You know the initial velocity, final velocity and retardation. Which kinematic equation to be used to find the displacement?

 

[avaholic]

To solve this problem mass is not necessary.
Which force is acting on the car while going up. Which component of this force retards the car? From that you can find the retardation.
You know the initial velocity, final velocity and retardation. Which kinematic equation to be used to find the displacement?

ok, now i feel like a dunce. gravity is acting on the vehicle, slowing it down at the g constant of 9.8 m/s.
i took 25 m/s and divided it by 9.8 m/s, giving me how long it took to stop, 2.55 seconds. i multiplied that by 25 m/s and got 63.77 m rounded up to 64m.

thanks

 

[rl.bhat]

ok, now i feel like a dunce. gravity is acting on the vehicle, slowing it down at the g constant of 9.8 m/s.
i took 25 m/s and divided it by 9.8 m/s, giving me how long it took to stop, 2.55 seconds. i multiplied that by 25 m/s and got 63.77 m rounded up to 64m.

thanks

The method is wrong. Some where you have to use the angle if inclination.

 

[avaholic]

The method is wrong. Some where you have to the angle if inclination.

gah... well I'm obviously lost

 

[rl.bhat]

The component of g along the inclined plane is g*sinθ.
Using the formula
vf^2 = vi^2 - 2*gsinθ*x, find x.