Why does the equationR=(V o 2 /g)sin2 (equation 3-18) not workfor this problem,

Question

Why does the equationR=(Vo2/g)sin2 (equation 3-18) not workfor this problem, with g being 9.81m/s, = 53 degrees, and R= 20m? Because it does not work, I looked at the way that was writtenonline for the solution. I do not understand how the problem jumpsfrom: -h = Vosin53(R/(Vocos53)) -(1/2)g(R/(Vocos53))2 to: R2g - Vo2sin(2x53)R -2hVo2cos253 I understand all except how theVo2sin(2x53) came to be. It appears to methat Vosin53/Vocos53 would produce somethingalong the lines of Votan53? Why does the equationR=(Vo2/g)sin2 (equation 3-18) not workfor this problem, with g being 9.81m/s, = 53 degrees, and R= 20m? Because it does not work, I looked at the way that was writtenonline for the solution. I do not understand how the problem jumpsfrom: -h = Vosin53(R/(Vocos53)) -(1/2)g(R/(Vocos53))2 to: Why does the equationR=(Vo2/g)sin2 (equation 3-18) not workfor this problem, with g being 9.81m/s, = 53 degrees, and R= 20m? Because it does not work, I looked at the way that was writtenonline for the solution. I do not understand how the problem jumpsfrom: -h = Vosin53(R/(Vocos53)) -(1/2)g(R/(Vocos53))2 to: to: R2g - Vo2sin(2x53)R -2hVo2cos253 I understand all except how theVo2sin(2x53) came to be. It appears to methat Vosin53/Vocos53 would produce somethingalong the lines of Votan53?

Explanation / Answer

This question is not a Horizontal Range problem. A rangeproblem launches and terminates at the same height. This problemlaunches from above the point where the projectile willland. For this particular problem you need to use two seperatekinematic equations. One for the x-component of the path and onefor the y-component of the path.       x-xo =Vox t    and   y-yo= Voy t -1/2gt2 Keeping in mind that:       Vox=Vo*cos() Voy=Vo*sin() and that t is the same at the end of the flight. So, solvethe x equation for t and substitute it into the y equation to findVo. Keeping in mind that:       Vox=Vo*cos() Voy=Vo*sin() and that t is the same at the end of the flight. So, solvethe x equation for t and substitute it into the y equation to findVo.

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