# The punter stands on the 22 yard (roughly a meter) line to the left of the 50 yard line and the ball is kicked with an initial velocity of 25.3 m/s at an angle of 58.5° above the ground. How high does the punt go?

The maximum height of the football is

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To find the maximum height of the punt, we can use the projectile motion equations. The formula to calculate the maximum height (Hmax) in projectile motion is:

Hmax = (v₀² * sin²(θ)) / (2 * g)

Where:

- v₀ is the initial velocity (25.3 m/s)
- θ is the angle of projection (58.5°)
- g is the acceleration due to gravity (9.81 m/s²)

Substituting the given values into the formula:

Hmax = (25.3² * sin²(58.5°)) / (2 * 9.81)

Calculate sin²(58.5°) ≈ 0.659 Hmax ≈ (25.3² * 0.659) / (2 * 9.81) Hmax ≈ (639.01 * 0.659) / 19.62 Hmax ≈ 21.34 meters

Therefore, the maximum height of the punt is approximately 21.34 meters.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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