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# The constant variables that are measured

### Introduction:

Basketball is a very popular game that can be played both outdoors and indoors. The main aim of the game is to score as many points as possible, in order to win. However, since it is a matter of getting the ball into the hoop in order to score points, the player has to determine the approximate size of angle ÆŸ in which he needs to shoot the ball so that he will have a high chance of scoring. The angle ÆŸ actually varies with the distance.

As we play basketball, we noticed that the farther the distance from the net, the angle ÆŸ in which the basketball travels to enter the net is smaller and the closer the distance from the net, the angle ÆŸ in which the basketball travels to enter the net is greater.

This is because the farther the shooter stands away from the net, the less acute the angle in which the ball travels in.

The aim of this study was to find out the relationship between the distance, d between the shooter and the basketball net affects the angle, ÆŸ (refer to Figure 1 below) at which the basketball is released. We have to assume that the force asserted on the ball is constant, the height at which the ball is being released is constant and the air resistance is constant.

### List of Variables:

### Independent Variable: The distance, d between the point of where the ball is released and the basketball hoop.

### Dependent Variable: The angle, ÆŸ in which the basketball is released.

### Variables to be kept constant:

- The height of the basketball hoop, h

- The size and mass of the mini basketball, m

- Distance from the starting position of ball to ground, H

- Gravitational Field Strength, g

- The force used to shoot the ball, F

- The speed of the wind

- Location of the experimental set-up (Sonia's living room)

### Constant variables that are measured:

Size and mass of the mini basketball, m = 17.0g

Height of basketball hoop, h = 28.5 cm

Distance from the starting position of ball (refer to Fig.1) to ground, H = 0.0m

Gravitational Field Strength, g = Assumed to be 9.8N/kg

Force used to shoot the ball, F = Maximum power of the hairdryer

### List of Apparatus needed:

-Mini basketball hoop (self-constructed)

-A mini-size basketball

-A long and heavy pole

-A retort stand with boss and clamp

-Meter Ruler

-Hairdryer and power supply for it to operate

-Protractor

### The Question:

How does the distance, d between the shooter and the basketball net affect the angle ÆŸ (refer to Figure 1 below)?

### Photos of Set-up

### Experimental Set-up (Diagram)

### Procedure:

- We would set up a mini basketball (court as shown in Fig. 1) whereby we would use a small basketball hoop that we constructed ourselves and a smaller sized basketball instead of the real basketball and hoop. We will set up this mini ‘basketball court' indoors(in Sonia's living room) so there will be less of an interference of wind and the air resistance will be reduced, or if not, remain constant at all times.
- We would then carry out the experiment using the mini basketball court. Firstly, we will measure the distance, d to be 1.50m (our starting distance).
- We will also measure the angle, ÆŸ in which the ball will travel to get to the hoop.
- We will then position the ball in the pole, at its starting position as shown in Figure. 1 and turn on the hairdryer to its maximum power.
- By looking at the parabolic curve made by the ball after being shot out through the other end of the pole, we will judge whether the angle ÆŸ that we have set originally is suitable or not. A suitable angle ÆŸ would mean that the angle in which the ball is released can make it travel the required distance, d to reach the hoop successfully.
- If the ball travels less than the required distance, d, we will decrease the angle ÆŸ by moving the boss and clamp down, so as to reduce the slanting of the pole, thus decreasing the angle ÆŸ. If the ball travels more than the required distance, d, we will increase the angle ÆŸ by moving the boss and clamp up, so as to increase the slanting of the pole, thus increasing the angle ÆŸ.
- We will keep experimenting and varying angle ÆŸ until we discover the optimum angle ÆŸ. The optimum angle ÆŸ is the angle in which the ball is released such that it can travel just the right distance to successfully reach the hoop and even score.
- After repeating the experiment four times with the optimum angle and make sure that the ball travels just the right distance, we will only record this optimum angle in the table below (we will not record other angles in which the experiment failed).
- We will repeat this whole experiment with varying distances, as shown in our table below.

### Results obtained

## d/m |
## Optimum Angle ÆŸ /degree |
## 1st Try |
## 2nd Try |
## 3rd Try |
## 4th Try |
## Percentage of ball getting in/ % |

1.50 |
45.0 |
Ball hits the hoop, did not get into the hoop |
Ball did get into the hoop |
Ball did get into the hoop |
Ball did get into the hoop |
75 |

1.30 |
49.0 |
Ball did get into the hoop |
Ball hits the hoop, did not get into the hoop |
Ball did get into the hoop |
Ball hits the board and bounced outwards, did not get into the hoop |
50 |

1.10 |
54.0 |
Ball hits the hoop. Did not get into the hoop |
Ball did get into the hoop |
Ball did get into the hoop |
Ball hits the hoop, did not get into the hoop |
50 |

0.90 |
60.0 |
Ball hits the hoop, did not get into the hoop |
Ball hits the hoop, did not get into the hoop |
Ball hits the hoop, did not get into the hoop |
Ball did get into the hoop |
25 |

0.70 |
65.0 |
Ball hits the hoop, did not get into the hoop. |
Ball gets into the hoop |
Ball hits the hoop, did not get into the hoop |
Ball did not get into the hoop |
25 |

0.50 |
70.0 |
Ball hits the hoop, did not get into the hoop |
Ball gets into the hoop |
Ball hits the hoop, did not get into the hoop |
Ball did not get into the hoop |
25 |

### Data Analysis

Through the results obtained from the experiment carried out, it shows that the further the distance the shooter is from the basketball net, the higher the chances of the ball getting into the hoop, provided that the angle ÆŸ is the optimum angle in which the ball is released. This also shows that the angle at which the ball is thrown at is another factor, which affects the chances of the ball entering the hoop. The smaller the angle ÆŸ, the higher the chances of the ball getting into the hoop.

We also noticed the decrease in percentage of the chance of the ball getting into the hoop as the distance, d becomes shorter and shorter.

### Discussion

From this experiment, we have come to a conclusion that in order to shoot from a further distance, the best angle ÆŸ to release the ball is 45Ëš, so that the ball will have a higher chance of entering the hoop. This knowledge will come in handy if someone wants to specialize in three-points shooting. To shoot a three-pointer, someone has to stand a very far distance(for example, 5.0m) from the hoop and in order to score, that person has to know that he cannot shoot the ball too high up(as in the angle ÆŸ being >45Ëš) or the ball will not travel far enough to even reach the hoop. Whereas if you are someone who wants to specialize in layups and since you have to score from under the basket, you have to shoot the ball high up in order to score, which means that the angle ÆŸ will be quite large(>60Ëš). However, we have also found out that when we shot the ball with a smaller distance away from the hoop, like (0.50m away from the hoop), it was actually quite hard for us to score and in fact, the scoring percentage is reduced greatly to around 25% only. Therefore, if someone wants to shoot the ball from under the basket, we would suggest that the person should shoot the ball in from the side. He can also use the board to his advantage by shooting the ball in from the side as the ball can bounce off from the board easily and into the hoop.

This whole idea of the basketball travelling in a parabolic curve is known as projectile motion. Projectile motion is the motion of an object whose path is affected by the force of gravity. We are all affected by gravity, but it profoundly alters the motion of objects that are thrown or shot upward. The parabolic curve of a thrown ball is caused by gravity and its falling motion in general.

Gravity is a force that acts on objects; it makes objects accelerate "downwards". We know that whenever an object is in the air it is being accelerated at 9.8m/sÂ² downward, but is there a corresponding horizontal acceleration? The only acceleration acting horizontally is deceleration due to air friction, this is often ignored and it is considered that there is no horizontal acceleration whatsoever. The only horizontal acceleration on an object happens when your hand accelerates it from rest, it is interesting to note that once an object leaves your hand it will not slow down horizontally.

Situations where an object is projected upward at an angle are much more common than those where an object is projected straight up or completely horizontally. Thus they are more useful to us.

How do we relate an object's takeoff velocity to its impact velocity? We know that the takeoff velocity and impact velocity have two components, the horizontal and vertical. We know that whenever an object is projected its horizontal velocity remains constant, while vertically it is accelerated at 9.8m/sÂ² [down].

The object starts its motion with a certain horizontal velocity and ends the motion with the same horizontal velocity. About the vertical velocity we know that when an object is thrown up it lands with the same speed as it left, therefore the only change in the components of the velocities (takeoff and landing) is that the vertical velocity is now in the downward direction. Since the magnitudes of the components are all the same, the speed of takeoff and landing will be identical. The only difference between the velocities is the direction - the impact velocity will have the same angle as the takeoff, only below the horizontal.

However, we had also spotted some errors that could have been present in our experiment to achieve the results that we have obtained. For example, whether the ball goes into the hoop also depended on whether the pole was facing straight at the hoop. To minimize this error, we made sure that for all experiments, the pole was positioned directly at the hoop. Another possible error would be the time taken to switch on the hairdryer to its maximum power. To minimize this error, we tried to switch on the hairdryer to its maximum at our fastest speed, we had also dedicated one specific person to switch the hairdryer on (Xin Ying) so that the time taken to switch the hairdryer on to its maximum power would most likely be about the same.

### Citations

### Acknowledgments

We would personally like to thank Mr. Ang for his patience to look through our draft report to correct our mistakes and to help us loan the necessary equipment from the physics lab for us to carry out our experiment.

### Personal Reflections

### Lim Xin Ying(16)

Through this SIA, I have actually learnt more about the physics that is involved in basketball (like projectile motion). It really taught me how I could actually improve my basketball skills by applying the laws of physics and now, I have a better understanding of the angle ÆŸ in which the ball should be shot at for a certain distance. Even though carrying out the experiment is quite tough as there are lots of apparatus to set up and a lot of things to take note about, but our final results proved to us that the experiments were worth it.

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