# Need work checked(dyanmics projectile problem)

• LightMech
In summary, the conversation is about a basketball player shooting a ball from a certain distance and angle, and the task is to find the initial velocity when the distance from the backboard is equal to 228mm and 420mm respectively. The conversation also includes a link to a picture for better understanding and a discussion about the correct values for X and Y in the equations used to solve the problem.
LightMech
First time poster, site looks very informative so I thought I would make a post. This is for Mechanics class and now covering Dynamics. This is my take home problem.

A basket ball player shoots when she is 5 m from the backboard. Knowing that the ball has an intial velocity Vo at an angle of 30⁰ with the horizontal, determine the value of Vo when d is equal to (a) 228 mm, (b) 420 mm.

## Homework Statement

given info:
x: player is 5M from back board
y: initial height of ball 2m from floor, hoop is 3.048m from floor
angle: 30⁰
d: this is the distance from the back board or offset

## Homework Equations

x = Vo cos(30)*t
y = Yo + Vo*sin(30)t - 1/2gt^2

## The Attempt at a Solution

x = 5m - .288m = 4.772m
4.772m = Vo*cos(30)*t
Vo = 4.772/cos(30)

y = 2m + (4.772m/cos(30))*sin(30)t - 1/2(9.81)t^2
t = .987s

Vo = 4.772/cos(30)*(.987s)
= 5.44m/s

Using same method
b = 5.13m/s
Found a picture for the problem on the net for better clarity:

Last edited by a moderator:
So its been several days now and no response. Perhaps I would have had better luck under the Physics section? If I did not explain the problem clearly I posted a link to the problem which includes a picture. I am pretty confident my work is correct but would feel a lot better if someone else can confirm this work accurate.

Equations look good, but check your math and you have a typo , should be Vo = 4.772/cos(30)*t (you left out the 't'). What value are you using for y?

I am solving for 't', so y = 0. But I use 2m for my Y0.
Here is a little more detail in my steps:
x = Vo cos(30)*t
4.772m = Vo*cos(30)*t
Vo = 4.772/cos(30)t
y = Yo + Vo*sin(30)t - 1/2gt^2
0 = 2m + (4.772m/cos(30))*sin(30)t - 1/2(9.81)t^2
(4.9)t^2 = (4.775)t^1/2
t = .987s
Vo = 4.772/cos(30)*(.987s)
= 5.44m/s

I am not sure about my value for 't'. I take the square root of both sides and solve for t, I get .987 when 4.9 over 4.775 or 1.013 when 4.775 over 4.9.

LightMech said:
I am solving for 't', so y = 0.
y is not 0 when the ball hits the basket.
But I use 2m for my Y0.
Here is a little more detail in my steps:
x = Vo cos(30)*t
4.772m = Vo*cos(30)*t
Vo = 4.772/cos(30)t
y = Yo + Vo*sin(30)t - 1/2gt^2
0 use correct value for y= 2m + (4.772m/cos(30)t)*sin(30)t - 1/2(9.81)t^2
you keep making the same error by omitting the t I've added in red.

Geeze I can't believe I mist that. Okay so:
Yo = 2m
Yf = 3.048m
3.048m = 2m + (4.772m/cos(30)t)*sin(30)t - 1/2(9.81)t^2
t = 1.7s
Vo = 4.772/cos(30)*(1.7s)
V0 = 9.37m/s

LightMech said:
Geeze I can't believe I mist that. Okay so:
Yo = 2m
Yf = 3.048m
3.048m = 2m + (4.772m/cos(30)t)*sin(30)t - 1/2(9.81)t^2
t = 1.7s
Vo = 4.772/cos(30)*(1.7s)
V0 = 9.37m/s
you seem to be having trouble with your math

1.048 = (4.772/cos30)sin30 -1/2(9.81)t^2

solve for t = ?

Ok, this is what I am doing:
4.9t^2= -1.048+(4.772/cos30)sin30 t's cancel on right side?
taking square toot to both sides and solving for t:
2.21t= 1.306
t=.59s

I am moving t^2 to the left side, I don't know why I am now getting different valudes for t.

LightMech said:
Ok, this is what I am doing:
4.9t^2= -1.048+(4.772/cos30)sin30 t's cancel on right side?
taking square toot to both sides and solving for t:
2.21t= 1.306
t=.59s

I am moving t^2 to the left side, I don't know why I am now getting different valudes for t.
Yes, that looks better. I'm not sure what you were doing before.

Thank you Phantom, I wasnt taking care of my 't' because I had it written incorrectly on a different set of notes. If I had took the time to think about it, I probably would have corrected it.

## What is a dynamics projectile problem?

A dynamics projectile problem is a type of physics problem that involves the motion of an object under the influence of gravity and other forces. It typically includes the initial velocity, angle of launch, and the height of the object.

## Why is it important to check work for dynamics projectile problems?

Checking work for dynamics projectile problems is important because it helps to ensure that the correct equations and values were used, and that the final answer is accurate. This is especially important in real-world applications where even small errors can have significant consequences.

## What are some common mistakes to watch out for when solving dynamics projectile problems?

Some common mistakes in solving dynamics projectile problems include using incorrect equations, not accounting for all the forces acting on the object, and making calculation errors. It is important to double-check all calculations and make sure all forces are considered.

## How can I check my work for dynamics projectile problems?

One way to check work for dynamics projectile problems is to use the same equations and values with different initial conditions and see if the results match. Another way is to use a graphing calculator or simulation software to plot the motion and compare it to the calculated values.

## Are there any tips for solving dynamics projectile problems more efficiently?

One tip for solving dynamics projectile problems more efficiently is to break the problem down into smaller parts and solve them separately. This can help to simplify the calculations and make it easier to identify and correct any mistakes. It is also helpful to practice and familiarize oneself with the equations and concepts involved.

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