### A skateboarder starts up a 1.0-m-high, 30° ramp at a speed of 6.9 m/s. The skateboard wheels roll without friction. At the top, she leaves the ramp and sails through the air.

### A) How far from the end of the ramp does the skateboarder touch down?

**SOLUTION:**

**PART A**

**ANSWER: 3.7 m**

This is a two-part problem. Use an s-axis parallel to the slope for the first part, regular xy-coordinates for the second. The skateboarder’s final velocity at the top of the ramp is her initial velocity as she becomes airborne.

Without friction, the skateboarder’s acceleration is . The length of the ramp is . We can use kinematics to find her speed at the top of the ramp:

This is the skateboarder’s initial speed into the air, giving her velocity components and . We can use the y-equation of projectile motion to find her time in the air:

This quadratic equation has roots -0.256 s and 0.797 s. The x-equation of motion is thus