A German V2 rocket from WW2 had a range of 300km, reaching a maximum height of 100km. What is the rocket's maximum initial velocity?
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you use a system of equations and solve for vi which is v initial
1: dy=vi1/2T+1/2aT the first 1/2 T is because your using a height of 100 which is half way through the parabolic motion, a is gravity or 9.81
2.dx=viT there is no 1/2at^2 because a=0 in the x direction
now you simply solve this system for vi the t's should cancel out