In the long jump, an athlete launches herself at an angle above the ground and lands at the same height, trying to travel the greatest horizontal distance. Suppose that on earth she is in the air for time *t*, reaches a maximum height *h*, and achieves a horizontal distance *D.*

If she jumped in exactly the same way during a competition on Mars, where *g*_{Mars} is 0.379 of its earth value, find her...

(a) time in the air.

(b) maximum height.

(c) horizontal distance.

This problem requires us to determine the **time **in the air, **maximum height**, and the horizontal distance (**range**) when the **gravitational acceleration** is changed.

Since the takeoff and landing are at the __same height__, this is a ** symmetrical launch** problem.

For **projectile motion problems in general**, we'll follow these steps to solve:

- Identify the
and__target variable__for each direction—remember that__known variables__*only*(Δ**3**of the**5**variables*x*or Δ*y*,*v*_{0},*v*,_{f}*a*, and*t*)*are needed*for each direction. Also, it always helps to sketch out the problem and label all your known information! __Choose a UAM__—sometimes you'll be able to go directly for the target variable, sometimes another step will be needed in between.**equation**for the target (or intermediate) variable, then**Solve**the equation__substitute known values__and__calculate__the answer.

In __step 2__, for the special case of a **symmetrical launch**, we also have equations for the **time** in air, horizontal distance traveled, also called the** ***range*, and

$\overline{)\mathit{t}\mathbf{=}\frac{\mathbf{2}{\mathbf{v}}_{\mathbf{0}}}{\mathbf{g}}\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{}\mathbf{\theta}}$, $\overline{){\mathit{R}}{\mathbf{=}}\frac{{{\mathit{v}}_{\mathbf{0}}}^{\mathbf{2}}\mathbf{}\mathbf{sin}\mathbf{\left(}\mathbf{2}\mathit{\theta}\mathbf{\right)}}{\mathit{g}}}$ and $\overline{){{\mathit{H}}}_{\mathit{m}\mathit{a}\mathit{x}}{\mathbf{=}}\frac{{{\mathit{v}}_{\mathbf{0}}}^{\mathbf{2}}\mathbf{}{\mathbf{sin}}^{\mathbf{2}}\mathit{\theta}}{\mathbf{2}\mathit{g}}}$

Projectile Motion: Positive Launch

Projectile Motion: Positive Launch

Projectile Motion: Positive Launch

Projectile Motion: Positive Launch