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.