The basketball passed through the hoop even
though it barely cleared the hands of the player B
who attempted to block it. Neglecting the size of the
ball, determine the magnitude 𝑣𝐴 of its initial
velocity and the height h of the ball when it passes
over player B.
To determine the magnitude of the initial velocity (vA) and the height (h) of the basketball when it passes over player B, we can use the principles of projectile motion.
Step 1: Identify the initial and final conditions:
- The initial condition is when the basketball is released from player A's hand.
- The final condition is when the basketball passes over player B's hands.
Step 2: Determine the known values:
We need to know the following information:
- The distance between player A and player B (let's call it d).
- The time it takes for the ball to travel from player A to player B (let's call it t).
- The acceleration due to gravity (g), which is approximately 9.8 m/s².
Step 3: Calculate the initial velocity (vA):
Since we are neglecting the size of the ball, we can assume that the basketball follows a parabolic trajectory. The horizontal distance traveled by the basketball is equal to the initial horizontal velocity (vA) multiplied by the time (t). Therefore, we can write:
d = vA * t
Solving for vA:
vA = d / t
Step 4: Determine the height (h) of the basketball when it passes over player B:
The vertical distance (h) can be calculated using the formula for the vertical motion of a projectile:
h = vA * t * sin(θ) - (1/2) * g * t^2
In this case, we neglect the size of the ball, so we don't need to consider any vertical velocities or angles. Therefore, the angle of projection (θ) is 0°, which means sin(θ) = 0.
Simplifying the equation for h:
h = - (1/2) * g * t^2
Step 5: Substitute values and solve:
Using the values of d and t, substitute them into the equations for vA and h to find the solutions.
Please provide the values for the distance between player A and player B (d) and the time it takes for the ball to travel from player A to player B (t), and I can calculate the magnitude of the initial velocity (vA) and the height (h) of the basketball when it passes over player B.