How Can I Solve a Projectile Motion Problem Without Knowing the Mass?

[saschouch]

I've been working on this for the past 3 days, and I have come up with no logical solution. Please help, even if it's just telling me how to set up my equations correctly, because I just can't seem to.

A sled with rider (no mass given) starts with an initial velocity of 4 m/s at the top of a hill that is inclined at 12 degrees with the horizontal. The hillside is 195m long, and the coefficient of friction between snow and sled is .06. At the bottom of the hill, the snow is level and the coefficient of friction is unchanged. There exists a 35 degree (from horizontal) ramp that is 5m long 30m from the bottom of the hill. How high does the rider get off of the ground?

If i had a mass, this wouldn't be so hard. Apart from struggling to find a force or final velocity, what can I possibly do? I have the whole KE=1/2mv^2 part started, and the PE=KE, but i have no idea where to go from there. i know that it is POSSIBLE to solve this without knowing mass, I just don't know how to really set it up correctly.

 

[Lucky14]

did you try using the mass equal to one and then the mass equal to any other number and seeing if the answer is different. Because if they don't give you a mass you should see if mass matters in the end.

 

[saschouch]

I'm certain that mass doesn't matter in the end. I also know that I will be needing to leave it as m in my equations, and just plugging those into other equations. I just don't know where to really start.

 

[sqrt(-1)]

First find the total energy for the system in terms of m. At the top of the slope we have

$$E_{tot} = \frac{1}{2}mv^2 + mgh = \frac{1}{2}m(4)^2 + m \times 9.81 \times 195 \sin(12)$$

now think about what's happened to the system in the course of the sled moving to the bottom of the slope.

 

[saschouch]

At the top of the slope, the KE should be zero, right? and at the bottom, the PE will be zero, and the KE will be the number that PE was at the top. What I am having trouble understanding is how to calculate the final velocity at the bottom of the slope, and how to use the force of friction/coefficient to determine how it will effect the velocity.

 

[sqrt(-1)]

He's already moving at 4m/s so his KE won't be zero at the top.

Next you should try and work out the magnitude of the normal reaction of the slope so that you can work out how much energy is lost to friction.

 

[saschouch]

ok, i'll try that. thanks a LOT for your help.