2-D Kinematics Question (Simple)

[mohabitar]

Homework Statement

A soccer ball is kicked with an initial horizontal velocity of 14 m/s and an initial vertical velocity of 15 m/s.

I have found the initial speed of the ball to be 20.51. That was the easy part. However, the next part is not working out for me. "What is the initial angle θ of the ball with respect to the ground?".

So I tried working backwords to find out what that angle is to the left of the right triangle. I used tanx=15/14. Why does this not work? I get 3.96 which I convert to degrees, to get 227degrees, but that's obviously wrong. Any idea as to where I can begin to solve this question?

 

[Doc Al]

I used tanx=15/14.

Good.

Why does this not work? I get 3.96 which I convert to degrees, to get 227degrees, but that's obviously wrong.

That should work just fine. Are you sure you pushed the right keys on your calculator? I don't see how you got 3.96.

 

[mohabitar]

Oh wow ok I did the calculation wrong. My calculator wasnt working so I just plugged that equation into wolframalpha to get the 227. Calculator started back up and used the inverse function to get it to work right. Thanks!

 

[mohabitar]

Ok now I am stuck at part two. "What is the maximum height the ball goes above the ground?".

The integral of velocity gives me position. That would be great if I could graph it, but I don't have any values for t. I tried finding the total horizontal displacement by using cos46.97=x/20.51 to give me the value of the Adjacent side in the triangle, then multiply by 2 to get full displacement, so that's 27.98. Set that equal to horizontal velocity to solve for t, get 2. Use t=2 in the vertical displacement equation to find total, to get 10.4 meters. That was the wrong answer however. Something seemed wrong about this method I did anyway. How can I go about finding t? Or even horizontal displacement?

 

[Doc Al]

Ok now I am stuck at part two. "What is the maximum height the ball goes above the ground?".

You would find it using the appropriate kinematic formula for accelerated motion. The key is to realize that the vertical and horizontal motions can be analyzed separately. The vertical motion is subject to the acceleration of gravity; the horizontal motion is not.

The integral of velocity gives me position. That would be great if I could graph it, but I don't have any values for t. I tried finding the total horizontal displacement by using cos46.97=x/20.51 to give me the value of the Adjacent side in the triangle,

That just gives you the horizontal component of the initial velocity--which you knew to begin with. Luckily, you can forget about the horizontal motion if all you want to know is the maximum vertical height.

What kinematic relationships have you studied? (Here's a short list: https://www.physicsforums.com/showpost.php?p=905663&postcount=2")

 

[mohabitar]

Havent really studied anything. Class just started, Mechanical Physics. I have never taken a physics class before, only Calc 1.

So which formula would I use? Velocity and Displacement? Dont really understand the format of the formula, how would I use it, if that's the one I should be using?

 

[Doc Al]

Havent really studied anything. Class just started, Mechanical Physics. I have never taken a physics class before, only Calc 1.

Your text must have a section on kinematics and projectile motion. Better look it over! (More references: http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html#mot1")

So which formula would I use? Velocity and Displacement?

That would be the easiest thing to do, but there are several ways to go.

Dont really understand the format of the formula, how would I use it, if that's the one I should be using?

Just look at your book's examples and give it a shot.