Question

Suppose the football from the example problem (v =₀ 20 m/s, o = 37.0o) was a punt, and left the punter’s foot at a height of 1.00 m above the ground. How far did the football travel before hitting the ground? Set x₀ = 0, y₀ = 0.

[Hint: yᶴ= -1 m, and so you will have to use the quadratic formula to find the time.]

Answer 1

To find the distance the football traveled before hitting the ground, we need to calculate the time it takes for the football to reach the ground. Using the kinematic equation and solving the quadratic equation, we find that the football traveled approximately 25.77 m.

Step-by-step explanation:

To find the distance the football traveled before hitting the ground, we need to calculate the time it takes for the football to reach the ground. The initial height (y₀) is 1 m and the final height (yᶴ) is -1 m (since the ground is at y = 0). Using the kinematic equation yᶴ = y₀ + v₀yt - (1/2)gt², we can plug in the values to solve for t.

-1 = 1 + (20sin37°)t - (1/2)(9.8)t²

By rearranging the equation and solving the quadratic equation, we find that t ≈ 1.47 s.

Now we can find the horizontal distance (x) traveled by using the equation x = v₀x * t. Since the ball was punted, the initial horizontal velocity (v₀x) is 20cos37°. Plugging in the values, we have x = (20cos37°) * 1.47 ≈ 25.77 m.