Final answer:
To find the meters the ball will be short of clearing the goal post, we can break down the initial velocity of the ball and calculate the horizontal and vertical components. By finding the time it takes for the ball to reach its maximum height and hit the ground, we can determine the total time of flight and the horizontal distance the ball travels. Subtracting this distance from the distance to the goal post will give us the meters the ball will be short.
Step-by-step explanation:
To find how many meters the ball will be short of clearing the goal post, we can break down the initial velocity of the ball into its horizontal and vertical components. The horizontal component can be found by multiplying the initial velocity by the cosine of the angle, and the vertical component can be found by multiplying the initial velocity by the sine of the angle. Using the vertical component, we can find the time it takes for the ball to reach its maximum height, and then we can find the time it takes for the ball to hit the ground. Knowing the total time of flight, we can find the horizontal distance the ball travels. Subtracting this distance from the distance to the goal post will give us the meters the ball will be short.
The horizontal component of the initial velocity is given by: Vx = V * cos(θ)
The vertical component of the initial velocity is given by: Vy = V * sin(θ)
The time it takes for the ball to reach its maximum height is given by: t = Vy / g
The total time of flight is given by: T = 2 * t
The horizontal distance the ball travels is given by: D = Vx * T
The meters the ball will be short of clearing the goal post is given by the difference between the distance to the goal post and D: Short = Distance to goal post - D