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

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

Range:

$\overline{){\mathbf{R}}{\mathbf{=}}\frac{{{\mathbf{v}}_{\mathbf{0}}}^{\mathbf{2}}\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{2}\mathbf{\theta}}{\mathbf{g}}}$

**Part A.**

From the third kinematic equation, a = 0 m/s^{2} since the velocity is constant for the motion in the first 2s.

Δx = v_{0}t = (7.00)(2.00) = 14.0 m

The total distance traveled by the ball is given by:

d = L + Δx = 18 + 14 = 32.0 m

This distance is covered in 2.00s

Using the third kinematic equation still and knowing that a = 0 m/s^{2},

v_{0x} = Δx/t = 32.0/2 = 16.0 m/s

A softball is hit over a third baseman's head with some speed v_{0} at an angle θ above the horizontal. Immediately after the ball is hit, the third baseman turns around and begins to run at a constant velocity V = 7.00m/s. He catches the ball t = 2.00s later at the same height at which it left the bat. The third baseman was originally standing L = 18.0m from the location at which the ball was hit.

Part A. Find v_{0}. Use g = 9.81 m/s^{2} for the magnitude of the acceleration due to gravity. Express the initial speed numerically in units of meters per second to three significant figures.

Part B. Find the angle θ in degrees. Express your answer numerically in degrees to three significant figures.

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