Short projectile motion question

a peron kicks a football from 39.6 meters from the goal posts. the kcik leaves the ground with a speed of 24.8m/s at an angle of 49.6 degrees. the goal post are 3.10 meters high

determine the amount by which the kick clears the goal posts

Calculate the height of the ball 39.6 meters from where it is kicked, and subtract 3.10 m from that.

These fomulas will come in handy:

The time it takes to reach the goal posts is
T = 39.6 meters/(Vo cos 49.6)

Football height at goal post =
(Vo sin 49.6* T) - (g/2) T^2

would the formula for solving for time be

vyf-vyi/a

To determine the amount by which the kick clears the goal posts, we need to calculate the maximum height reached by the football during its trajectory.

The horizontal and vertical components of the initial velocity can be calculated as follows:
Vx = V * cosθ
Vy = V * sinθ

Where:
V is the magnitude of the initial velocity (24.8 m/s)
θ is the angle of projection (49.6 degrees)

The time of flight can be calculated using the vertical component of the initial velocity:
t = 2 * Vy / g

Where:
g is the acceleration due to gravity (approximately 9.8 m/s^2)

Using the time of flight, we can calculate the maximum height reached by the football:
H = Vy^2 / (2 * g)

Now we need to determine if the goal post height is smaller, equal to, or higher than the maximum height. If the goal post height is higher, then the football clears the goal posts. Otherwise, it does not clear the goal posts.

Comparing the goal post height (3.10 meters) and the maximum height (H) will give us the answer.