2D Projectile Motion, kicking football

[enigmatic]

Kicking a football 36m from the goal, which is 3.05m high. The ball leaves the ground with a speed of 20m/s at an angle of 53 degrees to the horizontal. By how much does the ball clear or fall short of clearing the crossbar?



delta y = v₀cos(theta)delta t


The thing is, I don't know delta t, and the equation for delta t I have is delta t = delta x/ v₀cos(theta), but the only way of knowing delta x also requires delta t...

Can someone please walk me through the problem? (I can do the math myself but just what equations to use and such.) thanks a lot!

 

[tenicus]

To find delta t, use the equation:
v= (initial velocity) + a(t)

v= 0 at its maximum point
you know the initial vertical velocity (vo sin(theta)
and you know the accl due to gravity.
then multiply t by 2, since it is symmetric, to get the total time.

Sorry, I don't know how to do all the symbols and such.

 

[enigmatic]

TY for your reply.

I tried finding the time that way, but I ended up getting horribly negative numbers.

I then tried finding delta t by equaling it to delta x/ v₀cos(theta), where delta x = 36 and ended up getting t = 2.99s

I used that in the delta y equation of delta y = v₀sin(theta)delta t - (.5)(g)(delta t)² and was able to solve it from there.

This thread is solved but I'm not sure how to notate it as such...