Determine the Speed At Which the Basketball at A Must Be Thrown At The Angle Of 30 degree so that it make it to the basket B?

To determine the speed at which the basketball at point A must be thrown at an angle of 30 degrees so that it makes it to the basket B, we need to use the following equation of motion:

h = (v² sin² θ) / (2g)

where h is the height of the basket, v is the initial velocity of the basketball, θ is the angle at which the basketball is thrown, and g is the acceleration due to gravity (9.81 m/s²).

Assuming the height of the basket is 3.05 meters, we can plug in the values and solve for v:

3.05 = (v² sin² 30) / (2 * 9.81)

Simplifying the equation, we get:

v² = (2 * 9.81 * 3.05) / sin² 30

v² = 117.53

v = √117.53

v ≈ 10.84 m/s

Therefore, the basketball at point A must be thrown at a speed of approximately 10.84 m/s at an angle of 30 degrees to make it to the basket B.