Calculating Vo for a Basketball Shot at 40 Deg Angle

[warjunkie]

A 2.00m tall basket ball player is standing on the floor 10m from the basket. If he shoots the ball at 40 degrees angle with the horizontal, at what initial speed must he throw the basketball so that i goes through the hoop? The height of the basket is 3.05m.

Here how do i calculate for Vo?
i get t=10/(VoCOS40) and 1.05=(VoSIN40)t - 4.9t^2

 

[Kurdt]

Substitute that t into your y distance equation and do some manipulation so that V₀ is the subject.

 

[baba89]

To calculate the initial velocity (Vo) for the basketball shot, you will need to use the equations of motion for projectile motion. These equations are:

1. Vertical motion equation: y = yo + Voyt - 1/2gt^2

2. Horizontal motion equation: x = xo + Voxt

In this case, the vertical motion equation will be used to solve for the initial velocity (Vo). We know the following values:

- Initial vertical position (y0) = 2.00m (height of the player)
- Final vertical position (y) = 3.05m (height of the basket)
- Initial vertical velocity (Voy) = Vo*sin(40) (since the ball is thrown at an angle of 40 degrees)
- Time (t) = t (this is the time it takes for the ball to reach the basket)

Substituting these values into the vertical motion equation, we get:

3.05 = 2.00 + Vo*sin(40)*t - 4.9t^2

To solve for t, we can use the quadratic formula:

t = (-Voy +/- sqrt(Voy^2 - 4*(-4.9)*(2.05 - 2.00))) / 2*(-4.9)

t = (-Vo*sin(40) +/- sqrt(Vo^2*sin^2(40) + 19.6*(0.05))) / (-9.8)

Now, we can substitute this value for t into the horizontal motion equation:

10 = 0 + Vo*cos(40)*t

Solving for Vo, we get:

Vo = 10 / (cos(40)*t)

Substituting the value of t from the quadratic formula, we get:

Vo = 10 / (cos(40)*((-Vo*sin(40) +/- sqrt(Vo^2*sin^2(40) + 19.6*(0.05))) / (-9.8)))

This equation will give you the initial velocity (Vo) needed for the basketball to go through the hoop. You can choose the positive or negative value for t, depending on the direction you want the ball to go (i.e. towards or away from the player).