What Equation Determines the Velocity for a Basketball Shot?

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To determine the velocity needed for a basketball shot under ideal conditions, the discussion focuses on using kinematic equations of motion. Key parameters include an initial height of 6 feet, a trajectory angle of 45 degrees, a range of 14 feet, and a hoop height of 10 feet, with a total time of 2 seconds. The relevant equations involve calculating vertical and horizontal motion, specifically using v_y for vertical velocity and x(t) for horizontal distance. The user expresses confusion about the equations and their components, particularly regarding the meaning of v_y(t). Understanding these equations is essential for solving the problem effectively.
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Homework Statement


I don't know what equation to use. i am trying to find out the velocity need to make a shot. the conditions are ideal.
initial height: 6 feet
initial vertical velocity:unknown
angle of trajectory: 45 degrees
range: 14 feet
time:2 seconds
basketball hoop height: 10 feet

Homework Equations





The Attempt at a Solution


 
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Leonof said:

Homework Statement



I don't know what equation to use. i am trying to find out the velocity need to make a shot. the conditions are ideal.
initial height: 6 feet
initial vertical velocity:unknown
angle of trajectory: 45 degrees
range: 14 feet
time:2 seconds
basketball hoop height: 10 feet

Welcome to the PF. The Relevant Equations are the kinematic equations of motion for a constant acceleration (the acceleration due to gravity). Can you list those for us?

v_y(t) = _________

y(t) = __________

And you have a constant velocity in the x direction, so you can write:

x(t) = __________
 
xt=x0 + v0 cos(a) t
y(t) = y0 + v0 sin(a) t - (1/2) g t^2

i don't understand what is meant by v_y(t)
 
Leonof said:
xt=x0 + v0 cos(a) t
y(t) = y0 + v0 sin(a) t - (1/2) g t^2

i don't understand what is meant by v_y(t)

Good start. v_y is shorthand for the velocity in the y direction. Written more clearly in Latex:

v_y
 
v_y=vsin0-(gx/vcos0)
 
so 14+4cos45*2=18.2
-> 4sin45-(g*18.2/4cos45)?
 
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