QuestionJuly 17, 2025

A golf ball is struck across a flat fairway at an angle of 60^circ with an initial speed of 135ft/s a.). Write a set of parametric equations for the motion of the golf ball. b.). Determine how long the golf ball was in the air. c.). Determine how far the golf ball traveled in the air. Show all work. Use the Equation Editor. x=v_(0)cos(Theta )t Recall, y=-(1)/(2)(g)t^2+v_(0)sin(Theta )t+h g=32ft/sec/sec

A golf ball is struck across a flat fairway at an angle of 60^circ with an initial speed of 135ft/s a.). Write a set of parametric equations for the motion of the golf ball. b.). Determine how long the golf ball was in the air. c.). Determine how far the golf ball traveled in the air. Show all work. Use the Equation Editor. x=v_(0)cos(Theta )t Recall, y=-(1)/(2)(g)t^2+v_(0)sin(Theta )t+h g=32ft/sec/sec
A golf ball is struck across a flat fairway at an angle of 60^circ  with an initial speed of 135ft/s
a.). Write a set of parametric equations for the motion of the golf ball.
b.). Determine how long the golf ball was in the air.
c.). Determine how far the golf ball traveled in the air.
Show all work. Use the Equation Editor.
x=v_(0)cos(Theta )t
Recall, y=-(1)/(2)(g)t^2+v_(0)sin(Theta )t+h
g=32ft/sec/sec

Solution
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Answer

a.) x(t) = 67.5t, y(t) = -16t^2 + 116.865t ### b.) 7.30 seconds ### c.) 493.47 feet Explanation 1. Write Parametric Equations Use x = v_0 \cos(\Theta) t and y = -\frac{1}{2}gt^2 + v_0 \sin(\Theta) t + h. Given v_0 = 135 \, \text{ft/s}, \Theta = 60^\circ, g = 32 \, \text{ft/s}^2, and h = 0 (since the fairway is flat). x(t) = 135 \cos(60^\circ) t = 135 \cdot \frac{1}{2} t = 67.5t y(t) = -\frac{1}{2} \cdot 32 t^2 + 135 \sin(60^\circ) t = -16t^2 + 135 \cdot \frac{\sqrt{3}}{2} t = -16t^2 + 116.865t 2. Determine Time in Air Set y(t) = 0 to find when the ball hits the ground: -16t^2 + 116.865t = 0. Factor out t: t(-16t + 116.865) = 0. Solve for t: t = 0 or t = \frac{116.865}{16} = 7.3040625. 3. Calculate Distance Traveled Use x(t) with t = 7.3040625: x(7.3040625) = 67.5 \times 7.3040625 = 493.47 ft.

Explanation

1. Write Parametric Equations<br /> Use $x = v_0 \cos(\Theta) t$ and $y = -\frac{1}{2}gt^2 + v_0 \sin(\Theta) t + h$. Given $v_0 = 135 \, \text{ft/s}$, $\Theta = 60^\circ$, $g = 32 \, \text{ft/s}^2$, and $h = 0$ (since the fairway is flat).<br /> $x(t) = 135 \cos(60^\circ) t = 135 \cdot \frac{1}{2} t = 67.5t$<br /> $y(t) = -\frac{1}{2} \cdot 32 t^2 + 135 \sin(60^\circ) t = -16t^2 + 135 \cdot \frac{\sqrt{3}}{2} t = -16t^2 + 116.865t$<br /><br />2. Determine Time in Air<br /> Set $y(t) = 0$ to find when the ball hits the ground: $-16t^2 + 116.865t = 0$. Factor out $t$: $t(-16t + 116.865) = 0$. Solve for $t$: $t = 0$ or $t = \frac{116.865}{16} = 7.3040625$.<br /><br />3. Calculate Distance Traveled<br /> Use $x(t)$ with $t = 7.3040625$: $x(7.3040625) = 67.5 \times 7.3040625 = 493.47$ ft.
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