Basketball player shooting ball, finding velocity for a no backboard shot

In summary, the conversation discusses a basketball player attempting to make a basket from a distance of 10.8 m while avoiding the backboard. The equation 1/2((gd^2)/((cos(theta)^2 * ((H1-H2) +(d * tan(theta))) = Vo^2 is mentioned, but the individual is unsure of how to use it. The solution involves calculating the cosine and tangent of the angle of 47.2 degrees and using those values in the equation to find the initial speed needed to make the shot.
  • #1
BlazdNConfusd
2
0

Homework Statement


An h1 = 2.13 m tall basketball player wants to make a basket from a distance d = 10.8 m, as seen in the figure.

If he shoots the ball at α = 47.2° angle, at what initial speed must he throw the basketball so that it goes through the hoop without striking the backboard? The height of the basketball hoop is h2 = 3.05 m.


Homework Equations


1/2((gd^2)/((cos(theta)^2 * ((H1-H2) +(d * tan(theta))) = Vo^2


The Attempt at a Solution


I have absolutely no idea how to use that equation. I was horrible and dropped my trig class and in doing so completely forgot how to use equations with theta. Any help is greatly appreciated.
 
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  • #2
any ideas anybody? I've literally been working on this for hours
 
  • #3
Welcome to Physics Forums.

BlazdNConfusd said:

Homework Equations


1/2((gd^2)/((cos(theta)^2 * ((H1-H2) +(d * tan(theta))) = Vo^2
I'm not sure where that equation comes from, but (for now) will trust that it leads to the correct solution.

Make sure your calculator is in degrees mode (not radians), and calculate the following:

cos of 47.2 = ____?
tan of 47.2 = ____?

Then you can just plug those numbers in for cos(theta) and tan(theta).

On a TI 83+ calculator:

Select "degrees" mode:

MODE button
On 3rd line, put cursor on "Degree"
ENTER button -- "Degree" should be highlighted
2nd QUIT button

Calculate cosine of 47.2 degrees:

COS button
47.2
")" button
ENTER button

Hope that helps.
 

What is the velocity of a basketball player shooting a no backboard shot?

The velocity of a basketball player shooting a no backboard shot can vary depending on factors such as the player's strength, shooting technique, and distance from the basket. However, the average velocity for a standard basketball shot is around 20 miles per hour.

Can you calculate the velocity of a no backboard shot using a formula?

Yes, the formula for calculating velocity is velocity = distance / time. In order to calculate the velocity of a no backboard shot, you would need to measure the distance the ball traveled and the time it took to reach the basket. Then, you can use the formula to find the velocity.

How does the release angle affect the velocity of a no backboard shot?

The release angle can have a significant impact on the velocity of a no backboard shot. A higher release angle (closer to 90 degrees) will result in a higher velocity, while a lower release angle (closer to 0 degrees) will result in a lower velocity.

What other factors besides velocity can affect the success of a no backboard shot?

Other factors that can affect the success of a no backboard shot include the player's aim, the rotation of the ball, and external factors such as wind or distractions. Additionally, the player's physical strength, shooting technique, and experience can also play a role in the success of the shot.

Is there a specific technique for shooting a no backboard shot with maximum velocity?

Yes, there are various shooting techniques that can help a player achieve maximum velocity on a no backboard shot. These techniques include using the legs to generate power, keeping the elbow in while shooting, and following through with the wrist. Practicing these techniques and finding what works best for each individual player can lead to a more powerful and accurate no backboard shot.

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