1. Elma Muros Posadas was one of the country's best Elma Muros Posadas was one of the country best long jumpers. Suppose she makes a 30° angle with the ground before leaping. If her launch speed is 11m/s, compute the time of flight, the range and the maximum height reached. Given:
Required:
Solution:

Final

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Explanation:

Given:

  runner is launched at 30° angle to horizontal at 11 m/s

  acceleration due to gravity is g = -9.8 m/s²

Find:

  runner's hang time

  runner's distance to the landing point

  runner's maximum height

Solution:

The (horizontal, vertical) speed components will be ...

  (11 m/s)(cos(30°), sin(30°)) = (5.5√3 m/s, 5.5 m/s)

The time of flight can be found from the height formula:

  h(t) = 1/2gt² +vt . . . . . . where v is the vertical speed at launch

The time we're concerned with is the time when h(t)=0 and t>0.

  0 = -4.9t^2 +5.5√3t = t(-4.9t +5.5√3)

The second factor is zero when ...

  t = (5.5√3)/4.9 ≈ 1.122 . . . seconds hang time

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The distance to the landing point will be the product of horizontal speed and hang time:

  d = (5.5 m/s)(5.5√3/4.9 s) ≈ 10.693 m . . . . distance to landing

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The maximum height can be found from the formula (based on conversion of kinetic energy to potential energy) ...

  h = v²/|2g| = (5.5 m/s)²/(2(9.8 m/s²)) ≈ 1.543 m . . . . maximum height

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