If a projectile is launched from level ground, then the initial conditions are r(O) = 0
Chapter 9, Problem 16(choose chapter or problem)
If a projectile is launched from level ground, then the initial conditions are r(O) = 0, r'(O) = v0 = (v0cos O)i + (v0sin 8)j and the vector function (1) becomes r(t) = (v0 cos O)ti + [ ->2 + (v0 sin O)t]j. (6) This function is equivalent to the solution x(t), y(t) of the system of linear differential equations (8) in of Exercises 4.6 subject to the same initial conditions. Underlying that earlier discussion, as well as in the derivation of ( 1), is the assumption that the projectile is not subject to air resistance. Use (6) to show that the impact speed of a projectile is the same as the initial speed [[r'(O)[[ = [[v0[[ = v0 for any angle of elevation e, 0 < e < 90.
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