a kicker tries to make a field goal by kicking the ball over the goal post, which is 3.05 meters high. If he is 36 meters away and kicks the ball at 20 m/s and 53-degrees angle, will it go over the goal post? (show work)

Yes, the ball will go over the goal post by 0.769 meters

Explanation:

The given parameters are;

The height of the goalpost = 3.05 meters

The distance of the kicker from the goal post = 36 meters

The speed with which the ball is kicked, v = 20 m/s

The direction/path of the ball, θ = 53°

Therefore, we have;

The vertical component of the velocity, = v × sin(θ) = 20 × sin(53°) ≈ 15.973 m/s

The horizontal component of the velocity, vₓ = v × cos(θ) = 20 × cos(53°) ≈ 12.036 m/s

The time, t. to reach the goal post with the horizontal velocity is given as follows;

Time = Distance/Velocity = 36/12.036 ≈ 3 seconds

The height. h. of the ball at 3 seconds is given as follows;

h = × t - 1/2 × g × t²

h(3) = 15.973 × 3 - 1/2 × 9.8 × 3² = 3.819 m

The time to maximum height, is given as follows;

v = u - g·t

v = 0

u = 15.973 m/s

∴ u = g·t

15.973 = 9.8× t

t = 15.973/9.8 ≈ 1.63 seconds

Total time the ball stays in the air = 2 × 1.63 ≈ 3.26 seconds

Therefore, the ball is in the air at 3 seconds, and it will go over the goal post by 3.819 m- 3.05 m = 0.769 meters

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