Question

You are helping your friend prepare for the next skateboard exhibition by determining if the planned program will work. Your friend will take a running start and then jump onto a heavy-duty 13-lb stationary skateboard. The skateboard will glide in a straight line along a short, level section of track, then up a curved concrete wall. The goal is to reach a height of at least 10 feet above the starting point before coming back down the slope. Your friend's maximum running speed to safely jump on the skateboard is 24 feet/second. Your friend weighs 155-lbs. What is the height hf that your friend will reach according to his plan?

Answer 1

8.3 feet

Step-by-step explanation:

The kinetic energy of the system on the ground is ...

KE = Σ(1/2)(mv^2) = (1/2)(155)(24^2) +(1/2)(13)(0^2) = 44640 lb·ft²/s²

The potential energy at the highest point is the same:

PE = mgh

44640 = (155 +13)(32)h

h = 44640/5376 = 8.30 . . . . feet

_____

We haven't worried too much about the conversion between pounds mass and pounds force. Whatever factor may be involved will divide out when computing the maximum height. We have used g=32 ft/s².

__

To achieve a 10 ft height, the running speed would need to be 26.34 ft/s, about 10% higher.