Question

You project a basketball with an initial speed of 9 m/s and with an angle of 30.0∘ from the ground. It follows the parabolic trajectaory, and the ball enters the baslet in 2.0 s after it is launched. Ignor air resistanc!

a. Draw a carton, label your chosen origin, and label X and Y coordinates.
b. Calculate initial velocity on X and Y directions.
c. What will be acceleration on X and Y directions.
d. What is the horizontal distance from you to basket?
e. What height should be the basket located in your problem to catch the ball?
f. According to your calculated height, is it a real basketball problem, usual basket is located around 2−4 m above the ground? If not explain why?

Answer 1

(a) The diagram of the projectile is shown in the image attached.

(b) The initial velocity in X and Y direction is 7.8 m/s and 4.5 m/s respectively.

(c) The direction of the acceleration in Y direction is downward, while there is no acceleration is horizontal direction.

(d) The horizontal distance from you to the basket is 15.6 m.

(e) The height the basket should be located is 10.6 m.

(f) The height calculated is above is not real basket problem because it is greater than the height of a real basket.

How to calculate the initial velocity?

(b) The initial velocity in X and Y direction is calculated as;

Vx = 9 m/s x cos (30)

Vx = 7.8 m/s

Vy = 9 m/s x sin (30)

Vy = 4.5 m/s

(c) The acceleration on X and Y directions is determined as follows;

The direction of the acceleration in Y direction is downward, while there is no acceleration is horizontal direction.

(d) The horizontal distance from you to the basket is calculated as;

d = Vx x t

d = 7.8 m/s x 2 s

d = 15.6 m

(e) The height the basket should be located is calculated as follows;

h = Vyt - ¹/₂gt²

h = (4.5 m/s) x (2 s) - ¹/₂ x (9.8) x (2 s)²

h = -10.6 m

|h| = 10.6 m

(f) The height calculated is above is not real basket problem because it is greater than the height of a real basket.