Projectile motion - finding initial velocity with no time

[KKuff]

Homework Statement

I'm having trouble finding the initial velocity without knowing the time.

A basketball player is standing on the floor 10.0 m from the basket. The height of the basket is H = 3.05 m, and he shoots the ball at an angle, θ = 42.0°, with the horizontal from a height of h = 1.94 m. At what speed must the player throw the basketball so that the ball goes through the hoop without striking the backboard?

Homework Equations

I'm not sure how to determine which equations I need, since there are at least 2 variables that I don't know in each one

V(f) = V(i) + at
X(f) = X(i) + (1/2)(V(i) + V(f))t
X(f) = X(i) + V(i)t + (1/2)at^2
V(f)^2 = V(i)^2 + 2a(X(f) - X(i))

The Attempt at a Solution

I know that I have to break up the problem into x and y components. So I would have the y-velocity component Vy = Vsin42.0 and the x-velocity component Vx = Vcos42.0. I know that for the y component I would have an acceleration of -9.8m/s and that for the x component that I would have no acceleration since it is a constant velocity, so that would make Vx(i) = Vx(f). The initial horizontal position is X(i) = 0 and the final horizontal position is X(f) = 10. The initial vertical position is Y(i) = 1.94 and the final vertical position is Y(f) = 3.05.

I just don't know how to put all of this information together in order to find the initial velocity. Any help will be appreciated.

 

[tiny-tim]

Welcome to PF!

Hi KKuff! Welcome to PF!

(try using the X² and X₂ icons just above the Reply box )

Call the speed v, then find t from the x equation, and use that value of t in the y equation, to solve for v …

what do you get? ​

 

[KKuff]

I got about 10.6m/s. Thanks I appreciate it. Is t used since it would have the same value in both the x and the y components?

 

[tiny-tim]

Is t used since it would have the same value in both the x and the y components?

That's right!

(standard technique … sometimes it's t, sometimes it's x or y or even v )