Projectile Motion: Calculations for a successful basketball shot

In summary, The conversation discusses the assumption that the ball reaches the maximal height at the midpoint of its trajectory and the need for an argument to support this assumption. The use of a clearer diagram is suggested to better understand the concept, and it is mentioned that there could be alternative trajectories that would not affect the calculations. The speaker also mentions specific values for vertical and horizontal displacement and encourages the other person to try the question again using these values.
  • #1
ayderay
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0
Homework Statement
A basketball player shoots successfully at goal from a horizontal distance of 5.3m to the centre of the goal ring. She releases the ball at an angle of 48 to the horizontal and 1.2m below the height of the ring. What was the ball’s speed as it left her hand? The answer is 8.1m/s
Relevant Equations
Motion equations
4A14584B-3E5E-44EE-BA13-CE48F2DF1EC9.png
 
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  • #2
Why have you assumed that the ball reaches the maximal height at the midpoint of the trajectory? Can you make an argument for this?
 
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  • #3
Orodruin said:
Why have you assumed that the ball reaches the maximal height at the midpoint of the trajectory? Can you make an argument for this?
I assumed it..
 
  • #4
Perhaps a clearer diagram might help. We can ignore the practicalities of the hoop, and just consider the target as a point in space that we want to reach, at the top of the pole:

1587288195354.png


There is another trajectory you could have, I'll let you think of what that might be! It won't affect your calculations.
 
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  • #5
ayderay said:
I assumed it..
It is not a healthy habit to assume things that you cannot give an argument for. Can you show whether it is the case or not?
 
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  • #6
As the ball reaches the ring, how much is its horizontal displacement? How much is its vertical displacement?
 
  • #7
etotheipi said:
Perhaps a clearer diagram might help. We can ignore the practicalities of the hoop, and just consider the target as a point in space that we want to reach, at the top of the pole:

View attachment 260947

There is another trajectory you could have, I'll let you think of what that might be! It won't affect your calculations.
Ohh, thank u for this, it’s much more understandable. I’ll try the question out again
 
  • #8
ayderay said:
Ohh, thank u for this, it’s much more understandable. I’ll try the question out again
You treat 1.2m as displacement along vertical.
5.3 m as displacement along horizontal.
And proceed. You will get
 

1. How do you calculate the initial velocity of a basketball shot?

The initial velocity of a basketball shot can be calculated using the formula v = √(g * d / sin(2θ)), where v is the initial velocity, g is the acceleration due to gravity (9.8 m/s²), d is the horizontal distance from the shooter to the basket, and θ is the angle at which the ball is released.

2. What factors affect the trajectory of a basketball shot?

The trajectory of a basketball shot is affected by several factors, including the initial velocity, angle of release, air resistance, and the height and distance of the shot. Other factors such as the rotation of the ball and the release point on the shooter's hand can also have an impact.

3. How does air resistance affect the flight of a basketball?

Air resistance, also known as drag, can significantly affect the flight of a basketball. As the ball travels through the air, it experiences a force that slows it down due to the friction between the ball and the air molecules. This can cause the ball to drop faster and have a shorter overall distance traveled.

4. What is the optimal angle for a successful basketball shot?

The optimal angle for a successful basketball shot is around 45 degrees. This angle allows the ball to travel the furthest distance while still having enough height to clear the rim. However, the optimal angle may vary depending on the shooter's strength and shooting style.

5. Can you use projectile motion calculations to improve your basketball shooting?

Yes, projectile motion calculations can be used to improve basketball shooting. By understanding the physics behind a successful shot, players can adjust their technique, angle of release, and other factors to increase their chances of making a basket. Practice and experimentation can also help players find their optimal shooting angle and improve their overall accuracy.

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