Babe Didrikson holds the world record for the longest baseball throw (93.3m) by the woman. For the folowing question, assume that the ball was thrown at an angle of 50 degrees above the horizontal, that it traveled a horizontal distance of 90.3m, and that it was caught at the same level from which it was thrown. What was the ball's intital speed?
First off, identify your variables. You have your range (x-direction) and your angle of elevation. The basic motion equation is x= vo*t where vo is your initial veloity, x is range, and t is time of the entire flight. You can assume symmetry during the flight and therefore know that at peak height, the time of flight is t/2..... t=2t(peak).
At the peak of the flight curve, all your forces are in the vertical direction (y direction) and you know that 2t(peak)= 2(voy)/g where g is gravity. This yields to the ranging equation R= (vox*voy)/g = (2vo^2sin(theta)*cos(theta))/g which can be simplified to R= [vo^2*sin2(theta)]/g
remember sin2(theta) = 2sin(theta)*cos(theta)
Hope this helps!