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The height of the hurdler when he clears the hurdle is approximately 1.1045 meters (high)

Explanation:

The given parameters are;

The distance the hurdler is from the hurdle, d = 0.535 m

The velocity with which the hurdler jumps, u = 6.82 m/s

The angle at which the hurdler jumps, θ = 67.9°

The horizontal component of the velocity is uₓ = u × cos(θ)

∴ uₓ = 6.82 × cos(67.9°) ≈ 2.566 m/s

The time it takes, t, the hurdler to get to the hurdle horizontally 0.535 m away is given as follows;

Time, t = Distance/Velocity = d/uₓ = 0.535 m/(2.566 m/s) ≈ 0.2085 s

t ≈ 0.2085 s

The kinematic equation of vertical motion, under gravity can be presented as follows;

h = ·t - 1/2·g·t²

Where;

h = The height reached by the hurdler in time t

= The vertical component of the velocity = u × sin(θ)

g = The acceleration due to gravity

∴ = 6.82 m/s × sin(67.9°) ≈ 6.3189 m/s

≈ 6.3189 m/s

Substituting the known values gives;

h = 6.3189 × 0.2085 - 1/2×9.8×0.2085² ≈ 1.1045 m

The height of the hurdler when he clears the hurdle, h ≈ 1.1045 m.

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