Solving Physics Lab Challenge: Aim the Gun for the Cup

[mohlam12]

he everyone again!
today, i just got a lab for physics. I have two days to really examine that gun. the teacher will give me an angle that i should aim the gun, and a cup. I should know the distance between the gun and the cup so that when i launch the ball, it will go inside the cup...
first of all, i looked for "new" gravity, since there is air friction when the ball is launched, and i found that is 9.7m/ss , then I looked for the Initial velocity, i launched the ball vertically and i counted the time that took the ball to go upwards til it stops, then i counted the distance fron where it was lunched and where it stoped...after all, i found that the initial velocity is 6.69 m/s
Now, i am confised, first of all, can anyone tell me how is the angle of the gun related to the distance between where the gun is and where the ball landed after it was launched?
i tried to look for the time that it takes vertically for the ball when it is launched, i think i found .69sec that means that in .69 sec, the ball will go like v=d/t, (should i use the initial velocity for v?) if so, i found d=4.62m...
where do i have to use the angle...
also, i was very confused, so i decided to the a graph (the teacher said he is going to give me an angle to aim the gun between 30 and 60 degrees) so i launched the ball at 30,35,40,45,50,55,60 degrees, and i counted the distance the ball traveled, but i don t think that s a great idea since i ll have to launch the ball so it will go into the cup which is like 6cm of diameter, and to do that i have to be more accurate...
HEEEEEEEEEEEEEEEEEEEEEELP

 

[krusty the clown]

You need to use the angle to split up the initial velocity into components. I am not quite sure what you did to come up with the distance that you did.

The y component of the velocity experiences a constant acceleration. This allows you to find the time the ball is in the air. Then, using the x component and the time you can determine the distance it will travel.

Will the cup be at the same height as the gun?

Hope this helps.

Erik

 

[thepatientmental]

Hi there,

It sounds like you're on the right track with your initial calculations for finding the initial velocity and the time it takes for the ball to reach its peak height. To answer your question about the angle of the gun, it is related to the distance between the gun and the ball's landing position because the angle will determine the trajectory of the ball. The angle of the gun will affect the horizontal distance the ball travels, which is what you need to consider when trying to land the ball in the cup.

Using your calculated initial velocity and the time it takes for the ball to reach its peak height, you can calculate the horizontal distance the ball will travel using the formula d = v*t. This will give you the distance the ball will travel before reaching its peak height. However, you also need to consider the distance the ball will travel after reaching its peak height. This can be calculated using the formula d = 1/2 * a * t^2, where a is the acceleration due to gravity (9.8 m/s^2) and t is the time the ball is in the air. Adding these two distances together will give you the total horizontal distance the ball will travel.

As for using the angle, you can use it to determine the initial velocity in the x-direction (horizontal) and the y-direction (vertical). This can be done using trigonometric functions, specifically cosine for the x-direction and sine for the y-direction. Once you have the initial velocities in both directions, you can use them to calculate the horizontal and vertical distances as mentioned earlier.

It's great that you're using a graph to visualize the different angles, but as you mentioned, it may not be the most accurate method. You can continue to use the graph to get a general idea of how the angle affects the distance, but it would be best to use your calculated values for the most accurate results.

Hope this helps! Good luck with your lab.