A basketball leaves a player's hands at a height of 2.20 m above the floor. The basket is 2.70 m above the floor. The player likes to shoot the ball at a 36.0 ∘ angle. Of the shot is made from a horizontal distance of 9.10 m and must be accurate to ±0.23m (horizontally), what is the range of initial speeds allowed to make the basket

The range of initial speeds allowed to make the basket is: .

Explanation:

We must notice that basketball depicts a parabolic motion, which consists of combining a constant speed motion in x-direction and free fall motion in the y-direction. The motion is described by the following kinematic formulas:

x-Direction

y-Direction

Where:

, - Initial position of the basketball, measured in meters.

, - Final position of the basketball, measured in meters.

- Initial speed of the basketball, measured in meters per second.

- Time, measured in seconds.

- Tilt angle, measured in sexagesimal degrees.

- Gravitational acceleration, measured in meters per square second.

If we know that , , , , and , the system of equation is reduce to this:

(Ec. 1)

(Ec. 2)

At first we clear in (Ec. 1):

(Ec. 1) in (Ec. 2):

Now we clear the time in the resulting expression:

There are two solutions:

The initial velocity is cleared within (Ec. 2):

The bounds of the range of initial speed is determined hereafter:

The range of initial speeds allowed to make the basket is: .

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