Projectile motion - finding initial velocity with no time

AI Thread Summary
To find the initial velocity of a basketball shot without knowing the time, the problem can be broken into x and y components. The horizontal motion can be described using the equation for constant velocity, while the vertical motion incorporates gravitational acceleration. By solving for time using the horizontal motion and substituting that value into the vertical motion equation, the initial velocity can be determined. The calculated initial velocity required for the basketball to reach the hoop is approximately 10.6 m/s. This method effectively utilizes the relationship between the x and y components to solve the problem.
KKuff
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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.
 
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Welcome to PF!

Hi KKuff! Welcome to PF! :smile:

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

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

That's right! :smile:

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