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.

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