Optimistic Calculation of Ball Altitude

Have you ever wondered how to calculate the altitude at which a ball is kicked?

What equation can be used to determine the height of the ball?

Altitude Calculation Using Equations of Motion

When a ball is kicked with a velocity of 9m/s at an angle of 12 degrees from the horizontal and takes 4.0 s to reach the ground, we can calculate the altitude by utilizing the equations of motion and principles of trigonometry.

To calculate the altitude at which the ball is kicked, we can start by determining the initial velocity (upward component) using trigonometry. The initial velocity in the upwards direction is given by the formula u*sin(θ).

For this particular scenario, the initial velocity is equal to 9*sin(12 degrees), which results in approximately 1.89 m/s. Substituting this value into the equation h = ut - 0.5gt^2, where h is height, u is initial velocity, t is time, and g is the acceleration due to gravity (10 m/s^2), we can solve for the altitude.

By substituting the values into the equation, we get h = 1.89 m/s * 4 s - 0.5 * 10 m/s^2 * (4 s)^2, which simplifies to an altitude of around 67 meters. Therefore, the correct option is B, indicating that the altitude at which the ball is kicked is approximately 67 meters.