Running Down Ramps: Speed
When objects slide (frictionlessly) down a ramp, they’re acted on by a force, which means that they’re accelerated and therefore their speed changes. The equation to use in physics problems like these is
v_{f}^{2} – v_{o}^{2} = 2as
Finding the object’s final speed under these circumstances is easy when you remember that
s is the length of the ramp, and v_{o} is usually 0.
Sample question

Say you have a block of ice on a ramp at 20 degrees, and it slides down a ramp of 5.0 meters. What is its final speed at the bottom of the ramp?
The correct answer is 5.8 m/s.

The force along the ramp is

The acceleration of the ice is

Use the equation
Plug in the numbers: v_{f}^{2} = 34, which means v_{f} = 5.8 m/s.

Practice questions

Starting from rest, you go down a 100 m ski jump of 60 degrees. What is your speed at takeoff?

You’re heading down a toboggan run of 1 km at an angle of 18 degrees. What is your final speed?

You have a block of ice on a ramp with an angle of 23 degrees when it slips away from you. What is its speed at the bottom of the 6.0 m ramp?

A cart starts at the top of a 50m slope at an angle 38 degrees. What is the cart’s speed at the bottom?
Following are answers to the practice questions:

40 m/s

The force along the ramp is

Your acceleration is

Use the equation

Solving for v_{f} = 41 m/s. Round to 40 m/s to account for significant figures.


80 m/s

The force along the ramp is

Your acceleration is

Use the equation

Solving for v_{f} = 78 m/s. Round to 80 m/s to account for significant figures.


6.8 m/s

The force along the ramp is

The block of ice’s acceleration is

Use the equation

Solving for v_{f} = 6.8 m/s.


25 m/s

The force along the ramp is

The cart’s acceleration is

Use the equation

Solving for v_{f} = 25 m/s.
