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## Homework Statement

A quarterback claims that he can throw the football a horizontal distance of 169.1 m (185 yd). Furthermore, he claims that he can do this by launching the ball at the relatively low angle of 30° above the horizontal. To evaluate his claim, determine the speed with which this quarterback must throw the ball. Assume that the ball is launched and caught at the same vertical level and that air resistance can be ignored.

## Homework Equations

kinematics equations

## The Attempt at a Solution

First I cut the trajectory in half to find the footballs maximum height

than on the y coordinate is at its vertex its velocity at that point is 0 so i was able to put that in as well

So my list came out as is

X coordinate Y coordinate

X=84.55 Y=48.814

Xi=0 Yi=0

a=0 a=-9.8 m/s/s

Vi=? Vi=?

V=? V=0

than in order to get more information i solved for the ball to hit the ground from its highest altitude i.e. 48.814 meters.

dist = 1/2 g t^2 (g=9.8 m/s/s) so i used this equation and came up with 3.1562 seconds

Now I was able to solve for Vi for Y coordinate which i got 30.93m/s

after this i just used the sin(30)=30.93/x and i got 61.8628m/s

Was there an easier way to do this problem am i missing something very simple? but this answer is not matching up and cant seem to get it

thanks i advance