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Need some help on a projectile motion question.

## Homework Statement

Given:

- a football kicker can give the ball an initial speed of 25m/s

- kicker wants to score a field goal 50m in front of goalposts

- horizontal bar of goalposts is 3.44m above the ground

Question:

What are the a.) least and b.) greatest elevation angles at which he can kick the ball to score a field goal?

## Homework Equations

none

## The Attempt at a Solution

I have done the following:

1.) y = y

_{0}+ (v

_{0}sinθ)t - 0.5(9.81)t

^{2}

so, 3.44 = (25sinθ)t - 4.91t

^{2}

2.) x = x

_{0}+ (v

_{0}cosθ)t

so, 50 = (25cosθ)t

so, t = 2/cosθ

I then substituted eq. 2 into eq. 1, and got the following:

3.44 = 50tanθ - 19.62sec

^{2}θ

but I am stuck here.

Could someone please tell me if I am on the right track? Is there a way to solve the above equation, or am I approaching this in the wrong way?

Thanks.