Optimal kicking angle for maximum distance at 20 m/s

[Stephen Garner]

Homework Statement

The school football team has asked you for advice. During kickoffs the ball is not going far enough. The team's kicker shows you his kicks, and you figure out that he consistently kicks the ball so that it leaves his foot moving at 72 km/h.

a) Predict the best angle for him to try to kick the ball so that it will go as far as possible. [a: 45 degrees]

Homework Equations

X-component: cosΘ = adj/hyp
Y-Component: sinΘ = opp/hyp

v_f² = v_i²/ + 2ad

The Attempt at a Solution

I have converted 72 km/h to m/s.

72 * 1000 = 72000 / 3600 = 20m/s

I am confused because course has not asked us to predict an angle given such little data. Am I suppose to use gravity somewhere in here? I don't know how they arrived at 45 degrees.

 

[Orodruin]

How long will the ball be in the air? How far in the x-direction does it travel in that time? (Both as functions of the angle)

 

[Stephen Garner]

How do I figure out X-component if I don't have the angle though?

 

[Orodruin]

How do I figure out X-component if I don't have the angle though?

You write it as a function of the angle.

 

[Stephen Garner]

f(x) = 20x?

 

[haruspex]

f(x) = 20x?

No. Create an unknown to represent the angle. θ would be a standard choice.
Write the initial velocity components in terms of that.
Style tip: ignore the given speed of 20m/s for now. Just call it v. There are many advantages in not plugging in any numbers until the final step.

 

[Stephen Garner]

what numbers am I plugging into what? I'm more confused than before. x + y = 180?

 

[haruspex]

what numbers am I plugging into what? I'm more confused than before. x + y = 180?

If the kicker kicks the ball at a speed v and an angle θ to the horizontal, what are the vertical amd horizontal components of its initial velocity?