Provide an Appropriate Response $3.1$ Feet Above the Ground $150 \mathrm { ft } / \mathrm { sec }$

Multiple Choice

Provide an appropriate response.
-A baseball is hit when it is $3.1$ feet above the ground. It leaves the bat with an initial speed of $150 \mathrm { ft } / \mathrm { sec }$ , making an angle of $24 ^ { \circ }$ with the horizontal. Assuming a drag coefficient $k = 0.12$ , find the range and the flight time of the ball. 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 $\left( 32 \mathrm { ft } / \mathrm { sec } ^ { 2 } \right)$ .

A) Flight time = 3.97 sec; range = 424.4 feet
B) Flight time = 3.74 sec; range = 413.5 feet
C) Flight time = 2.82 sec; range = 393.5 feet
D) Flight time = 3.62 sec; range = 402.2 feet