Answer to Question #143379 in Physics for Ron Ace P. Morris

Question

A kicked football leaves the ground at an angle θ = 45⁰ with the horizontal has an initial speed of 25 m/s. Determine the distance of X. Acceleration due to gravity is 10 m/s².

Answer 1

Let's first find the time that the football takes to reach the maximum height from the kinematic equation:

$$v_y=v_0sin\theta-gt_{rise},$$ $$0=v_0sin\theta-gt_{rise},$$ $$t_{rise}=\dfrac{v_0sin\theta}{g}.$$

Then, we can find the total flight time of the football:

$$t=2t_{rise}=\dfrac{2v_0sin\theta}{g}.$$

Finally, we can find the horizontal range of the football from the kinematic equation:

$$x=v_0tcos\theta=v_0cos\theta\dfrac{2v_0sin\theta}{g}=\dfrac{v_0^2sin2\theta}{g},$$ $$x=\dfrac{(25\ \dfrac{m}{s})^2\cdot sin2\cdot 45^{\circ}}{10\ \dfrac{m}{s^2}}=62.5\ m.$$

Answer:

$x=62.5\ m.$