What angles will allow the football to clear the crossbar?

[terryaki]

Here's a problem that I just can't seem to get. I just need to get started out.

A placekicker is about to kick a field goal. The ball is 26.9 m from the goalpost. The ball is kicked w/ a initial velocity of 19.8 m/s at an angle theta above the ground. Between what two angles, theta1 & theta2, will the ball clear the 2.74-m-high crossbar?

What am I looking for here? Do I even get the question?

This is my interpretation: What is the angle of intersection if I draw a horizontal line 2.74-m-high off the ground to the path of the ball? I'm guessing I'm going to have to use Vnaught*cos(theta). Is that what I'm supposed to figure out? If that is, how (just nudge me in the right direction)?

 

[Sonty]

Just a nodge, right? I'll try. Do you agree the path of the ball will be a parabola? Think that if you kick the ball at a very small angle it will reach the goal very fast but it will also touch the ground very close to where you kicked it. It you kick it to high it will go up, get lost in the sunlight and still fall short of the goal that it might not even reach. So you must give it enough horizontal speed to reach the goal and enough vertical speed to clear the post. You're looking for the 2 solutions of a second degree equation with the variable sinθ

 

[HallsofIvy]

You are correct that the initial HORIZONTAL speed is v0 cos(theta) and the initial VERTICAL speed is v0 sin(theta).

You will need to write out the equations for height (y-component) and horizontal distance (x-component) of the football (I'll bet those are given in your book). Use the x- formula to determine the time, t, when the ball passes the goal posts. Now use the y- formula to determine the height at that time. Finally, determine what values of theta will make the height (at that time) 26.9 meters or more.