Calculating Initial Velocity for Accurate Basketball Shot

AI Thread Summary
To calculate the initial velocity required for a basketball shot, the player shoots from a height of 2.15m towards a basket at 3.05m, at a 40-degree angle and a horizontal distance of 10m. The vertical distance is 0.9m, and the shot must be accurate within ±0.32m horizontally. The projectile motion equation y = yo + x*tanθ - 1/2*g*x²/(v*cosθ)² is relevant for solving this problem. The discussion highlights the need to determine the correct application of projectile motion equations to find the initial velocity. Understanding these concepts is crucial for accurately calculating the required speed for making the basket.
Alserina
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Homework Statement


A basketball leaves a player's hands at a height of 2.15m above the floor. The basket is 3.05m above the floor. The player likes to shoot the ball at a 40-degree angle.

If the shot is made from a horizontal distance of 10.00m and must be accurate to +0.32m (horizontally), what is the range of initial speeds allowed to make the basket?


Homework Equations


sinx = opposite side/hypotenuse


The Attempt at a Solution


What I attempted to do was draw two right-angled triangles /| with a 40-degree angle, a 0.9m vertical side and a variable horizontal side (9.68m/10.32m) and tried to figure out the hypotenuse, but it doesn't seem right...
 
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What is the relevant equation of the projectile motion?
 
final velocity = initial velocity + (9.80)(time)? I don't really get which p.m. equation would apply...
 
Alserina said:
final velocity = initial velocity + (9.80)(time)? I don't really get which p.m. equation would apply...
The equation can be written as
y = yo + x*tanθ - 1/2*g*x2/(v*cosθ)^2
Solve for v.
 

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