How High Will a Toboggan Go Up an Icy Hill?

[bertoline]

Homework Statement

At the base of a frictionless icy hill that rises at 29.0deg above the horizontal, a toboggan has a speed of 12.0 m/s toward the hill. How high vertically above the base will it go before stopping?

Homework Equations

Wtot=K2-K1
K=1/2mv^2
K2=1/2mv^2=K1+Wtot

The Attempt at a Solution

Vx=12cos(29) = 10.5 m/s
vf^2-vi^2=2as
0-(10.5)^2=2(-9.8)s
s= 5.625

 

[AFG34]

This is how i would do it:
1. draw an fbd of the toboggan
2. use f=ma to solve for a
3. solve for distance traveled on the hill
4. then you make a triangle, with the distance you found in 3) being the hypotenuse, solve for the vertical side, and that's how high it has travelled.

 

[Moetasim]

m vertically above the base



Based on the given information, it can be calculated that the toboggan will travel approximately 5.625 m vertically above the base of the hill before coming to a complete stop. This is derived from the equations of motion, where the initial kinetic energy of the toboggan is equal to the work done by gravity to bring it to a stop at the highest point of the hill. It is important to note that this calculation assumes a frictionless and icy surface, which may not be realistic in real-world scenarios. Factors such as air resistance, surface roughness, and temperature could affect the actual distance traveled by the toboggan. Further experiments and calculations may be needed to accurately determine the height reached by the toboggan in different conditions.