Football related Projectile problem

[Go Angels]

Homework Statement

A placekicker must kick a football from a point 36.0 m (about 40 yards) from the goal, and half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 20.0 m/s at an angle of 48.0° to the horizontal.
(a) By how much does the ball clear or fall short of clearing or fall short of clearing the crossbar? (Enter a negative answer if it falls short.)

Homework Equations

Possibly:
vxi = vi cos theta
vyi = vi sin theta
change(y) = viy(t) + .5(a)(t)^2

The Attempt at a Solution

20 sin 48(t) - 4.9(t)^2
= 26.75-4.9(1.8)^2
change(y) = 26.75 - 15.88 =10.87

10.87-3.05 = 7.82 m. Which is the wrong answer.

Can someone please help. Thanks

 

[Doc Al]

Start by figuring out the time it takes for the ball to reach the goal. Hint: Consider the horizontal motion.

 

[Go Angels]

time = (vi sin theta) / g

Is that the correct equation?

So it's (20 sin 48) / 9.8 = 1.52

I plugged that in and obtained 8.21 m as my finals answer, which is incorrect. Can some please tell me what I did wrong?

 

[Doc Al]

No, that's not correct. Hint: The horizontal component of motion is unaccelerated. (Gravity only acts downward.)

What's the speed in the horizontal direction?

 

[Go Angels]

(20 cos 48) / 9.8?

 

[Doc Al]

(20 cos 48) / 9.8?

Why divide by 9.8? (Check your units.)

 

[Go Angels]

Opps, I thought I was still looking for time.

Why would I need to know the speed though, since the velocity is already given.

I basically just plug everything into the R = (vi^2 sin 2theta)/g equation right?

 

[Doc Al]

Opps, I thought I was still looking for time.

That's what we're heading towards calculating.

Why would I need to know the speed though, since the velocity is already given.

Then when I asked for the speed in the horizontal direction you should have answered without hesitation.

I basically just plug everything into the R = (vi^2 sin 2theta)/g equation right?

Nope. That's a range equation.

Start with what I suggested in post #2.

 

[rocomath]

The Range equation only applies to situations when your initial and final y values are the same. In other words, y is unchanged.