Provide an Appropriate Response $3.2$ Feet Above the Ground $152 \mathrm { ft } / \mathrm { sec }$

question 18

Multiple Choice

Provide an appropriate response.
-A baseball is hit when it is $3.2$ feet above the ground. It leaves the bat with an initial speed of $152 \mathrm { ft } / \mathrm { sec }$ , making an angle of $18 ^ { \circ }$ with the horizontal. Assuming a drag coefficient $\mathrm { k } = 0.12$ , how high does the ball go, and when dc it reach maximum height? For projectiles with linear drag:
$$\begin{array} { l } x = x _ { 0 } + \frac { v _ { 0 } } { k } \left( 1 - e ^ { - k t } \right) \cos \alpha \\y = y _ { 0 } + \frac { v _ { 0 } } { k } \left( 1 - e ^ { - k t } \right) \sin \alpha + \frac { g } { k ^ { 2 } } \left( 1 - k t - e ^ { - k t } \right) \end{array}$$
where $\mathrm { k }$ is the drag coefficient, $\mathrm { v } _ { 0 }$ and $\alpha$ are the projectile's initial speed and launch angle, and $g$ is the acceleratic of gravity $\left( 32 \mathrm { ft } / \sec ^ { 2 } \right)$ .

• A) Maximum height = 3.48 feet;
• B) Maximum height = 0.21 feet; time to maximum height = 0.05 sec time to maximum height = -0.21 sec
• C) Maximum height = 3.51 feet;
• D) Maximum height = 8.71 feet; time to maximum height = 0.02 sec time to maximum height = 0.74 sec

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