# Find Initial Velocity of Projectile Basketball

## Homework Statement

An 1.94 m tall basketball player wants to make a basket from a distance d = 19.8 m. If he shoots the ball at θ = 58.7° angle, at what initial speed must he throw the basketball so that it goes through the hoop without striking the backboard? The height of the basketball hoop is 3.05 m.
ΔH(y) = 1.11 m
d(x) = 19.8 m
θ = 58.7°
a(y) = -9.81 m/s^2

## Homework Equations

x(t) = X_0 + V_0x*t
v(y) = V_0y - g*t
v_f^2 = v_i^2 + 2a*d

## The Attempt at a Solution

0 = V_iy^2 + 2(-9.81)(1.11) → 4.66 m/s
0 = 4.66 + (-9.81)t → 0.475 s
V_0 = 4.66/sin(56.2) → 5.61 m/s
This is not the correct final answer and i am not sure where to even start with this problem

## Answers and Replies

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Why is v_f = 0?

You can't just plug numbers into equations, you need to think about what you are doing. This is a projectile motion problem. There are two coordinates in this case that need to be thought about. What is the common variable between the x and the y that you can use to find the velocity that will allow the basketball to reach the hoop without hitting the backboard?

Edit: I'm sorry, clearly you are thinking, it's just that you need to really think ahead is what I meant. You need to identify the problem, think about what kind of conditions need to be satisfied in order for the basketball to reach the net, etc.

You can't just plug numbers into equations, you need to think about what you are doing. This is a projectile motion problem. There are two coordinates in this case that need to be thought about. What is the common variable between the x and the y that you can use to find the velocity that will allow the basketball to reach the hoop without hitting the backboard?

Edit: I'm sorry, clearly you are thinking, it's just that you need to really think ahead is what I meant. You need to identify the problem, think about what kind of conditions need to be satisfied in order for the basketball to reach the net, etc.
I have been working on this problem for 2 hours and no matter what i try i get the same answer and it is the wrong answer. The only thing i think to try to set equal is time (t) and every time i do that i get the initial velocity as 14.4 m/s and that is incorrect.

## Homework Statement

An 1.94 m tall basketball player wants to make a basket from a distance d = 19.8 m. If he shoots the ball at θ = 58.7° angle, at what initial speed must he throw the basketball so that it goes through the hoop without striking the backboard? The height of the basketball hoop is 3.05 m.
ΔH(y) = 1.11 m
d(x) = 19.8 m
θ = 58.7°
a(y) = -9.81 m/s^2

## Homework Equations

x(t) = X_0 + V_0x*t
v(y) = V_0y - g*t
v_f^2 = v_i^2 + 2a*d

## The Attempt at a Solution

0 = V_iy^2 + 2(-9.81)(1.11) → 4.66 m/s
0 = 4.66 + (-9.81)t → 0.475 s
V_0 = 4.66/sin(56.2) → 5.61 m/s
This is not the correct final answer and i am not sure where to even start with this problem
I was recently stumped on this same kind of question. This is a miserable question without knowing about a certain concept. This concept should be in your textbook. It is very surprizing and even interesting.

It is very hard to explain without a diagram, but there should be an explanation in your textbook. It should have something to do with a projectile aimed at something that will fall at the same time that the projectile is fired. The interesting thing is that the two objects will meet at some point under the object that falls. This is the key to understanding your question.

Try to imagine how that concept works for your question.

I have been working on this problem for 2 hours and no matter what i try i get the same answer and it is the wrong answer. The only thing i think to try to set equal is time (t) and every time i do that i get the initial velocity as 14.4 m/s and that is incorrect.
This is a classic projectile motion problem. If you understand the concept, all the problems are the same. The key thing to understand about these problems is that there is no acceleration in the x direction. If you throw a basket ball with a certain horizontal velocity, there is no force acting on it to change that velocity until it comes into contact with the net. The other key thing to know is that in order for this basketball to hit the net without hitting the backboard, the basketball must reach the net in the x direction at the same time as the y direction. If the ball reached the net at a different time in the x than it did in the y, then it would either go over/under the net the moment it covered the distance in the x, or it would fall short/hit the backboard/pass over the net the moment it was at the right height.

Try solving the problem with these concepts in mind.

Thank you all for your help i was able to use the equation range = (velocity^2*sin2(theta))/g, where g is positive 9.81 to get the correct answer.