1. One application of integration of (2D) vector functions is in ideal projectil

Question

1. One application of integration of (2D) vector functions is in ideal projectile motion. If a projectile is launched with initial velocity v0 (measured in feet/sec) and launch angle ? and we assume that the only outside force that acts on the projectile is the force of gravity, then we get that the acceleration vector for the projec- tile is ?a(t) =< 0,?32 > and the initial velocity vector for the projectile is ?v(0) =< v0 cos(?), v0 sin(?) >.

(a) Use the above information to find the position function for the projectile given that the projectile is launched from the origin. [5 points]

(b) Find the maximum height that the projectile reaches. [5 points]

(c) Find the time at which the projectile hits the ground (as- suming that the ground is always at a height of 0). [5 points]

Explanation / Answer

1. One application of integration of (2D) vector functions is in ideal projectil

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