Uniform accelerated motion (UAM) equations, a.k.a. "kinematics equations":

$\overline{)\mathbf{}{{\mathit{v}}}_{{\mathit{f}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathbf{}}{\mathbf{-}}{\mathit{g}}{\mathit{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathit{y}}{\mathbf{=}}{\mathbf{}}\mathbf{\left(}\frac{{\mathit{v}}_{\mathit{f}}\mathbf{+}{\mathit{v}}_{\mathbf{0}}}{\mathbf{2}}\mathbf{\right)}{\mathit{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathit{y}}{\mathbf{=}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathit{t}}{\mathbf{-}}\frac{\mathbf{1}}{\mathbf{2}}{\mathit{g}}{{\mathit{t}}}^{{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}{\mathbf{}}{{{\mathit{v}}}_{{\mathit{f}}}}^{{\mathbf{2}}}{\mathbf{=}}{\mathbf{}}{{{\mathit{v}}}_{{\mathbf{0}}}}^{{\mathbf{2}}}{\mathbf{}}{\mathbf{-}}{\mathbf{2}}{\mathit{g}}{\mathbf{\u2206}}{\mathit{y}}}$

**(a)**

Time is determined by motion in the y-direction.

- t = t
_{w} - g
- Δy = - h
- v
_{0y}= 0

From the third UAM equation:

At a local swimming pool, the diving board is elevated h = 25.5 ft above the pool's surface and overhangs the pool edge by L = 6 ft. A diver runs horizontally along the diving board with a speed of v_{0} = 13.7 ft/s and then falls into the pool. Neglect air resistance. Use a coordinate system with the horizontal x-axis pointing in the direction of the diver’s initial motion, and the vertical y-axis pointing up.

**Part (a) **Enter an expression for the time t_{w} it takes the diver to fall off the end of the diving board to the pool's surface in terms of v_{0}, h, L, and g.

**Part (b)** Calculate this time, t_{w} in seconds.

**Part (c)** Determine the horizontal distance, d_{w} in feet, from the edge of the pool to where the diver enters the water.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Intro to Projectile Motion: Horizontal Launch concept. You can view video lessons to learn Intro to Projectile Motion: Horizontal Launch. Or if you need more Intro to Projectile Motion: Horizontal Launch practice, you can also practice Intro to Projectile Motion: Horizontal Launch practice problems.

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Based on our data, we think this problem is relevant for Professor McGill & Ray's class at UF.