Question

A golfer drives golf ball with a velocity of100 ft/sec and an angle of 45 degrees.
Find the time of travel.
Find the balls range.
Find the max height of the ball

Answer 1

1) Velocity equation in vertical axis:

$$v = v _ {0} \sin a - g t$$

its known, that initial and final vertical velocity are equal in magnitude, but opposite in direction, so

$$\begin{array}{l} - v _ {0} \sin a = v _ {0} \sin a - g t \\ t = \frac {2 v _ {0} \sin a}{g} \\ t = \frac {2 * 30.48 * \sqrt {2}}{2 * 9.8} = 4.4 (s) \\ \end{array}$$

2) Coordinate equation in horizontal axis:

$$\begin{array}{l} S = v _ {0} \cos a * t \\ x = 30,48 * \frac {\sqrt {2}}{2} * 4.4 = 94.8 (m) \\ \end{array}$$

3) Ball reaches the maximum height at the time $t/2$, so:

$$\begin{array}{l} h = v _ {0} * \frac {t}{2} - \frac {g \left(\frac {t}{2}\right) ^ {2}}{2} \\ h = 30.48 * \frac {4.4}{2} - \frac {9.8 \left(\frac {4.4}{2}\right) ^ {2}}{2} = 43.3 (m) \\ \end{array}$$