Basketball shot with just x and y distance and angle

[IAmPat]

Homework Statement

At its farthest point, the three-point line is 7.24 meters away from the basket in the NBA. A basketball player stands at this Int point and releases his shot from a height of 2.05 meters at a 35.0 degree angle. The basket is 3.05 meters off the ground.
The player wants the ball to go directly in (no bank shots). At what speed should he throw the ball?

Change in Y = 1 meter
Change in X = 7.24 meters
Angle Theta = 35.0
Vx = ?
Vy = ?
Voy = Initial Y Velocity
Vox = Initial X Velocity
t = ?

Homework Equations

Vox = Vo * Cos(35)
Voy = Vo * Sn(35)
Change Y = Voy*t + 1/2*(-9.8)*(t^2)

The Attempt at a Solution

Been attempting for days. I feel like I don't have enough information to complete the problem. If I had the initial x or y velocity, or the time it took to get from 0 to 7.24 I could do the problem easily, but I don't know how to get those with just this information.

I need to find the velocity at which he should shoot to make it straight into the basket

 

[tiny-tim]

Hi Pat!

(have a theta: θ and try using the X² icon just above the Reply box )

call the speed v, and do x and y equations separately, to find t

(obviously, it has to be the same t !)

then eliminate t ​

 

[IAmPat]

Hi Pat!

(have a theta: θ and try using the X² icon just above the Reply box )

call the speed v, and do x and y equations separately, to find t

(obviously, it has to be the same t !)

then eliminate t ​

I'm confused as to which x and y equations you're referring to. Won't I still not have enough information to get any of the variables?

 

[tiny-tim]

(just got up :zzz: …)

I'm confused as to which x and y equations you're referring to.

Sorry … by x I meant horizontal, and by y I meant vertical.

Won't I still not have enough information to get any of the variables?

Try it and see!

 

[rwisz]

, correct?

I would approach this problem by first identifying the known variables and using the appropriate equations to solve for the unknowns. In this case, the known variables are the change in x and y distance, the angle of release, and the initial height of the ball. The unknowns are the initial x and y velocities, as well as the time it takes for the ball to reach the basket.

To solve for the initial x and y velocities, we can use the equations Vx = Vo * Cos(35) and Vy = Vo * Sin(35). This will give us the components of the initial velocity in the x and y directions. We can then use the equation Change Y = Voy*t + 1/2*(-9.8)*(t^2) to solve for the time it takes for the ball to reach the basket. Once we have the time, we can use it to solve for the initial x velocity using the equation Change X = Vox * t. Finally, we can use the Pythagorean theorem to find the magnitude of the initial velocity, which is the speed at which the player should throw the ball to make it directly into the basket.

It is important to note that these equations assume a perfect environment with no air resistance and a perfectly flat surface. In reality, the ball's trajectory will be affected by air resistance and the surface of the court, so the calculated speed may not be exact. However, this approach will provide a good estimate for the required speed and can be adjusted for real-life conditions.