Problem 482 A skateboarder starts up a 10mhigh 30 ramp at a

Problem 4.82

A skateboarder starts up a 1.0-m-high, 30? ramp at a speed of 5.3m/s . The skateboard wheels roll without friction. At the top, she leaves the ramp and sails through the air.

PartA:

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

Express your answer to two significant figures and include the appropriate units.

l=_Value__Unit___

Solution

First, I would find out Vy1, and Vx.

To do that, we do:
Vy1 = 5.3sin30
=2.65m/s

Vx = 5.3cos30
=4.589m/s
Remember, velocity for x for projectile motion is always constant!

We already know Displacement y=1m (given) and ay = 9.8m/s^2 (assuming it\'s on Earth), so now we can solve for time.

D = V1y*t + 1/2a*t^2
1 = 2.65*t + 1/2(9.8)*t^2
0 = 4.9t^2 + 2.65t - 1

This is a quadratic..and when you solve for the roots you get:
t = 0.256s .. or t = -1 which we don\'t use, as time can\'t be negative.

So, now we can solve for displacement of x (what we want) with t=0.256s and Vx=4.589
Dx = Vx*t
Dx = 4.589*0.256
Dx = 1.175m

Thus 1.175m is your answer. hope that helps!