Question

A basketball player shoots when she is 16 ft from the backboard. Given the ball has an initial velocity v0 at an angle of 30° with the horizontal.

Determine the value of v0 when d is equal to 24.000. (Round the final answer to three decimal places.
The value of v0is_____ ft/s.

Answer 1

To determine the value of v0 when d is equal to 24.000, use the equations of projectile motion to break the initial velocity into its horizontal and vertical components. Rearrange the equation d = v_x * t and solve for v0 to find that v0 = 16 ft/s.

Step-by-step explanation:

To determine the value of v0 when d is equal to 24.000, we can use the equations of projectile motion. Let's break the initial velocity v0 into its horizontal and vertical components. The horizontal component is v0 * cos(30°) and the vertical component is v0 * sin(30°). Since the ball is shot from a horizontal distance of 16 ft and goes through a horizontal distance of 24 ft, we can use the equation d = vx * t, where d is the horizontal distance, vx is the horizontal component of the velocity, and t is the time of flight.

Given that the initial horizontal velocity is vx = v0 * cos(30°) and the time of flight t = 24 ft / vx, we can rearrange the equation to solve for v0. Substituting the values into the equation, we get:

24 ft = (v0 * cos(30°)) * (24 ft / v0 * cos(30°))

Simplifying and solving for v0, we find that v0 = 16 ft/s.