Solving for Time and Max Height of a Kicked Football

[kk727]

Question: 1. A football is kicked towards a field goal 28m away. The initial velocity of the ball is 37 m/s. The ball crosses safely through the uprights, while it is 3m above the ground.
a. Find time when it passes through the uprights.
b. Find its max height.
c. Find its launch angle.

Homework Equations

v = v_o + at
x = x_o + v_ot + 1/2at²

The Attempt at a Solution

So, we started this problem in class today, and didn't have enough time to solve it completely.
We first split the velocity into its X and Y components:
V_oY= 37sinθ
V_oX=37cosθ

Using V=x/t, we figured out that 37cosθ=28/t, and t=28/37cosθ.

Then using this equation, we plugged in everything that we had.
3 = 0 + 37sinθt - 4.9t²
3 = 0 + 37sinθ(28/37cosθ) - 4.9(28/37cosθ)²

We attempted to solve for t by plugging in 28/37cosθ for it, but ended up getting a bunch of trig, and I personally couldn't solve it. Can anyone help out? Is everything at least right up to here? Thanks in advance!

 

[zgozvrm]

Forget about plugging in the values of [itex]V_{oy}[/tex] and [itex]V_{ox}[/tex] for now ... just use the variables in your equations.

For example, with V = x/t, try using [itex]V_{ox} = \frac{28}{t}[/tex]
and go from there. Your calculations will be much easier!

 

[kk727]

Thank you so much! That's something that I've been struggling with for a while now, because we've been doing a lot of problems like that in class, and it frustrates me when I end up with this giant, ugly equation! You're right, it's muuuuuch easier!

 

[zgozvrm]

Thank you so much! That's something that I've been struggling with for a while now, because we've been doing a lot of problems like that in class, and it frustrates me when I end up with this giant, ugly equation! You're right, it's muuuuuch easier!

No problem!

You should have come up with 2 answers for each question. What did you get?

 

[kk727]

Oh, sorry, I forgot to check this again! I don't remember, because I don't have my notebook with me, but we went over it in class and I had it right! Everyone else had big long trig equations that they were trying to solve and I felt so smart! Hahaha, thanks again!