Answer:
The vertical velocity of the ball when released = 10.81 m/s
The vertical velocity of the ball in the basket = 8.81 m/s
Explanation:
The given parameters are;
The height of the basket = 10 feet
The horizontal location of the shooter from the basket = 20 feet
The height from which the shooter releases the ball = 8 feet
The horizontal velocity of the ball = 10 ft/s
Therefore, we have;
Time, t = Horizontal distance/(Horizontal velocity)
t = 20/10 = 2 seconds
The vertical velocity is given as follows;
s = u·t - 1/2·g·t²
Where;
u = The vertical velocity
s = The height above the initial height from which the ball is released
s = y - y₀
Where;
y = The final height of the ball in the calculation = The height of the basket = 10 foot
y₀ = The initial height from which the ball is released = 8 feet
∴ s = 10 - 8 = 2 feet
g = The acceleration due to gravity = 9.81 m/s²
Substituting gives;
2 = u × 2 - 1/2 × 9.81× 2²
u = (2 + 1/2 × 9.81× 2²)/2 = 10.81 m/s
The vertical velocity of the ball when released = 10.81 m/s.
The vertical velocity of the ball in the basket is given by the following relation;
v² = u² - 2·g·s
v² = 10.81² - 2×9.81×2 = 77.6161
v = √(77.6161) = 8.81 m/s
The vertical velocity of the ball in the basket = 8.81 m/s