Antrox said:
It's possible to solve physics problems when everything is unknown: initial speed, angle, coeff of friction, height gained. The solution, however, will be a function of all the variables. That, after all, is what the equations of motion are: general equations, where all quantities are unknown.
So, it must be possible to solve this problem. The answer will be a function of all the variables. So, it might be something like:
v (at bottom of slope) = velocity at start - gh*coeff of friction*tan(angle) - ... (some long complicated function)
There's nothing stopping you working out this formula, even if it gets very complicated.
But, it's possible that it doesn't get complicated at all! It's possible that things like angle and coeff of friction might cancel out and leave a simple formula.
How I started was this:
Let ##u## be the initial velocity at the bottom of the slope (u = 3m/s)
Let ##h## be the height gained (h = 0.3m)
Let ##\theta## be the angle of the slope
Let ##s## be the distance traveled up the slope
Let ##\mu## be the coefficient of friction.
Let ##g## be the acceleration due to gravity.
Let ##v## be the final velocity at the bottom of the slope.
I then worked out ##v## in terms of ##u, h, \theta, s, \mu \ and \ g##
But, ##\theta, s, \mu## all canceled out, leaving me with a nice equation for ##v## in terms of ##u, g \ and \ h##
Then, of course, I plugged ##u = 3## and ##h = 0.3## into the equation.
This is a good problem, as it shows the power of maths and general formulas to solve problems, even if you only know some of the variables.