Law of Conservation of Energy Problem (kicking a soccer ball)

[orangegalaxies]

Homework Statement

A soccer player kicks the ball in a parabolic arc to the opposite goal. The ball leaves the player’s foot at a speed of 27m/s, making an angle of 20 degrees above the horizontal. The mass of the ball is 0.43kg.

a. Determine the maximum height of the ball’s trajectory.
b. Determine the speed of the ball 3.5 m above the ground.

Relevant Equations

Ek = 1/2(m)v^2
Eg = mgh

a) So far, I have equated Ek to Eg to solve for h. 1/2(m)(27)^2 = m(9.8)h. I haven't taken the angle into consideration. I'm not sure if I have to use the x or y component. I got my answer to be 37m but again I don't believe this is correct.

b) I did Ek = Eg + Ek. 1/2(m)(27)^2 = m(9.8)(3.5) + 1/2(m)(v^2). I got v = 26m/s but I don't know if this is the right way to do it since I didn't use the angle again.

 

[PeroK]

a) So far, I have equated Ek to Eg to solve for h. 1/2(m)(27)^2 = m(9.8)h. I haven't taken the angle into consideration. I'm not sure if I have to use the x or y component. I got my answer to be 37m but again I don't believe this is correct.

b) I did Ek = Eg + Ek. 1/2(m)(27)^2 = m(9.8)(3.5) + 1/2(m)(v^2). I got v = 26m/s but I don't know if this is the right way to do it since I didn't use the angle again.

For a) don't you think the angle is important?

For b) you could check your answer using components if you're really not sure.

 

[haruspex]

For a) don't you think the angle is important?

E.g., what if the angle were zero?

 

[Delta2]

for b) your approach and equation is correct(I haven't checked your exact arithmetic though). Since we are interested in the speed of the ball (magnitude of velocity) we can just use conservation of energy.

for a) you say that $\frac{1}{2}mv^2=mgh$ however this equation is missing something. At the highest point of the trajectory, doesn't the ball still have some kinetic energy? How much is this kinetic energy at the highest point ? If you answer correctly you ll see why the angle matters.

 

[haruspex]

I got v = 26m/s

Since you are only given the initial speed to two sig figs, you are right to round it to 26, but it's a bit unsatisfactory because that makes it look as though the loss of speed is 1m/s, whereas it is about 1.3m/s. Had I set the question I would have said the initial speed was 27.0m/s.