Challenge: Basketball Shot Simulator
To deepen your understanding of projectile motion, you will now simulate a basketball shot and determine if it successfully passes through a hoop at a specified location. This challenge uses the equations of projectile motion to model the path of the basketball, considering its initial speed and launch angle. By applying these principles, you will write a Python function to predict whether the shot results in a score, based on the ball's trajectory and the hoop's position.
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Write a function basketball_shot_scores(...) that determines whether a basketball shot is successful based on a simplified projectile motion model.
The function receives:
initial_speed— the launch speed of the ball in meters per secondlaunch_angle_deg— the launch angle in degreeshoop_x,hoop_y— the horizontal and vertical position of the hoophoop_radius— optional reminder radius, default0.23meters
What you must do
-
Assume the ball is launched from point
(0, 0). -
Model the ball’s motion using standard projectile motion equations under gravity (
g = 9.81 m/s²). -
Determine whether the shot is successful by checking horizontal reach only:
- Compute the horizontal range of the shot.
- The shot is considered successful if the ball reaches the hoop’s
x-position (within a tolerance based onhoop_radius).
-
Return:
Trueif the ball can reach the hoop horizontally.Falseotherwise.
Important clarifications
- You do not need to simulate the full trajectory step-by-step.
- You do not need to check the ball’s exact height at the hoop (
hoop_yis provided for completeness but does not affect the result). - The function must always return a boolean value.
Output
Return a single boolean value indicating whether the shot scores.
Solução
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Can you explain the equations of projectile motion involved in this scenario?
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To deepen your understanding of projectile motion, you will now simulate a basketball shot and determine if it successfully passes through a hoop at a specified location. This challenge uses the equations of projectile motion to model the path of the basketball, considering its initial speed and launch angle. By applying these principles, you will write a Python function to predict whether the shot results in a score, based on the ball's trajectory and the hoop's position.
Swipe to start coding
Write a function basketball_shot_scores(...) that determines whether a basketball shot is successful based on a simplified projectile motion model.
The function receives:
initial_speed— the launch speed of the ball in meters per secondlaunch_angle_deg— the launch angle in degreeshoop_x,hoop_y— the horizontal and vertical position of the hoophoop_radius— optional reminder radius, default0.23meters
What you must do
-
Assume the ball is launched from point
(0, 0). -
Model the ball’s motion using standard projectile motion equations under gravity (
g = 9.81 m/s²). -
Determine whether the shot is successful by checking horizontal reach only:
- Compute the horizontal range of the shot.
- The shot is considered successful if the ball reaches the hoop’s
x-position (within a tolerance based onhoop_radius).
-
Return:
Trueif the ball can reach the hoop horizontally.Falseotherwise.
Important clarifications
- You do not need to simulate the full trajectory step-by-step.
- You do not need to check the ball’s exact height at the hoop (
hoop_yis provided for completeness but does not affect the result). - The function must always return a boolean value.
Output
Return a single boolean value indicating whether the shot scores.
Solução
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