Question

Hope and Sae are trying to decide if they should buy a new skateboard or not. They want a skateboard that gives them the longest jump in the air off a ramp they've built. The new skateboard's designer claims to have an aerodynamic design that allows the longest air time possible when used correctly. Hope and Sae's old skateboards don't have this aerodynamic design. They wonder if this is true and decide that Hope will buy the new skateboard to try out and Sae will wait to see how it works before she buys one or not.

Answer 1

When they think about the longest jumps, the aerodynamics of such a small thing as a skateboard is not that important as the angle of launch. According to the following expression, the longest jump ever at any speed will be achieved if they jump at a 45° angle:

$$R=\frac{v^2\text{ sin}(2\theta)}{g}.$$

No matter what velocity will it be, the velocity is nothing is the angle is not 45° because

$$\text{sin}(2\cdot45°)=\text{sin}90°=1,\\\space\\ R=\frac{v^2}{g}.$$

The range is maximum if the angle is 45 degrees.