- #1

Niriz

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## Homework Statement

A kicker is attempting a field goal from 50 m from the goal posts, which are 3.44 m high. He can kick the ball with initial speeds of 25 m/s. Ignoring air resistance, within what angular range must he kick the ball to score?

## Homework Equations

Pf = Pi + Fnet*t

And any equations which can be derived from this (the kinematics formula)

## The Attempt at a Solution

I've tried several approaches to this question but none of them seem to be able to neatly isolate one trigonometric function with a number. However I have come up with a few statements that I think should be true:

25m/s = (Vy^ + Vx^)^(1/2) since the components must equal 25 m,

And we know that Vy = sinθ*25 m/s while Vx = cosθ*25 m/s

The time it takes for the ball to reach the goalpost should equal 2/cosθ s, since it must travel 50 metres at a velocity of cosθ*25m/s.

For minimum angle I was thinking that, in time t, the vertical distance it travels must be 3.44 m, so I used the formula d = vi*t + (1/2)at^, so

3.44 m = sinθ*25*(2/cosθ) + 0.5(-9.8m/s^)(2/cosθ)^

But this does not turn simplify into a very nice formula... And is it right of me to think this? One of the biggest issues I'm having is not being able to produce a number for any velocity, because it could be any range of time or distance before Vfy = 0...

Any push in the right direction would be greatly appreciated! Such as another relationship equation...

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