a golf ball travels a distance of 600 feet as measured along the ground and reaches an altitude of 200 feet. If the origin represents the tee and the ball travels along a parabolic path that opens downward, find an equation for the path of the golf ball.

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Y = y0 + V0y * t + gt^2 / 2

y0 = 0

g ≈ - 32 ft / s^2

(1) y = V0y * t - 16t^2

(2) x = V0x * t

Use (1) and the maximum heigth formula to determine V0y

y max = (V0y) ^2 / (2g) = 200 = > (V0y) ^2 = 2*32*200 = 12,800 = > V0y ≈ 113.14 ft/s

y = 113.14 t - 16t^2

for y = 200 = > 200 = 113t - 16t^2 = > - 16t^2 + 113.14t - 200 = 0

Solve that equation using the quadratic formula and you will ge t = 3.54 s

The total time is 3.54 s * 2 = 7.08 s

Then use that time in (2) to find V0x

600 = V0x * t = > V0x = 600 / 7.08 s = V0x = 84.7 ft/s

Then, x = 84.7 t.

Now solve for t and replace it in y = 113.14 t - 16t^2:

t = x / 84.7

y = 113.14 (x/84.7) - 16 (x^2 / 84.7 ^2) = 1.336 x - 0.00223x^2

You can check that for, except for a small difference due to the approximations, for x = 600, y = 0 and for x = 300 y = 200

Answer: y = 1.336 x - 0.00223x^2