Long Jumper Analysis: How Far Can They Move Horizontally?

How far does a long jumper move horizontally with a height of 3.6 m and a horizontal velocity of 8.0 m/s?

The distance that the long jumper moves horizontally can be calculated using the formula: distance = velocity x time. Given that the long jumper achieves a height of 3.6 m and a horizontal velocity of 8.0 m/s, we can calculate the time the jumper spends in the air and determine the horizontal distance covered.

Calculating Time in the Air

To calculate the time the long jumper spends in the air, we can use the vertical motion equation: y = v_i t + 1/2 a t^2.
  • y: 3.6 m (height achieved by the long jumper)
  • v_i: 0 m/s (initial velocity, as the jumper starts from rest)
  • a: acceleration (unknown)
  • t: time spent in the air
By substituting the known values into the equation, we find that the long jumper spends 0.856 seconds in the air.

Calculating Horizontal Distance

With the time in the air known, we can use the horizontal velocity to calculate the distance travelled. The formula for distance is: distance = velocity x time. Substituting the given values and solving for time, t = 0.856 seconds.
  • Substitute time t = 0.856 seconds into the formula for distance:
  • d = 8.0 m/s x 0.856 s = 6.85 meters
Therefore, the long jumper moves 6.85 meters horizontally.
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