A baseball pitcher releases the ball horizontally from a height of 5 ft with an initial speed of 140 ft/s. Find the height of the ball when it reaches home plate 60 feet away. Round to two decimal places. (Hint: Determine the time of flight from the x-equation, then use the y-equation to determine the height.)
A) 2.33 ft
B) 2.06 ft
C) 3.67 ft
D) 2.67 ft

Question

Quizplus · Accepted Answer

The time of flight can be found using the horizontal motion equation $x = v_xt$, where $x = 60$ ft and $v_x = 140$ ft/s, giving $t = \frac{60}{140} = \frac{3}{7}$ seconds. For vertical motion, use $y = y_0 + v_{y0}t - \frac{1}{2}gt^2$, where $y_0 = 5$ ft, $v_{y0} = 0$ (since the ball is released horizontally), and $g = 32$ ft/s$^2$. Plugging in the values, $y = 5 - \frac{1}{2} \cdot 32 \cdot (\frac{3}{7})^2$, which calculates to approximately 2.06 ft.

A Baseball Pitcher Releases the Ball Horizontally from a Height