Two golf balls are hit into the air at 80 feet per second (60 mi/hr), making angles of 31 degrees and 49 degrees with the horizontal. If the ground is level, estimate the horizontal distance traveled by each golf ball.

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Step-by-step explanation:

The vertical height as a function of time for some initial velocity v and some launch angle α is ...

  h = (-16t +v·sin(α))t

This will be zero (the ball hits the ground) at ...

  t = v·sin(α)/16

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The horizontal distance as a function of time is then ...

  x = v ·cos(α)t

Where t is given from the height equation, the horizontal distance to the point where the ball hits the ground is ...

  x = v·cos(α)·v·sin(α)/16 = v²·sin(2α)/32

For an angle of 31°, the ball will travel ...

  (80 ft/s)²·sin(62°)/(32 ft/s²) = (200 ft)·sin(62°) ≈ 176.6 ft . . . at 31° angle

For an angle of 49°, the ball will travel ...

  (200 ft)·sin(98°) ≈ 198.1 ft . . . at 49° angle

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