12.3.10 Evaluate 0/2[(acost)^+(asint)^+k^]dt12.3.11Findr(t)thatsatisfiestheinitialconditionr(t)=4e2t^+3et^,r(0)=2^ 12.3.12 Find r(t) that satisfies the initial condition r(t)=1+t21^+t21^+t1k^,r(1)=2^ 12.3.13 Use ideal projectile motion concepts to find the initial speed of a projectile launched from the origin at an angle of measured from the horizontal if it just barely cleared a wall at a distance d feet from the origin and h feet high. The maximum height is the vertical component of the position vector at t=gv0sin. 21g(gv0sin)2+v0sin(gv0sin)=21gv02sin2+gv02sin2=21gv02sin2 Find the formula for the flight time of a projectile The time of flight must be twice the time when the projectile reaches maximum height. Find the formula for the range of a projectile The range or maximum distance is the horizontal component of the position vector at t=g2v0sin. v0cos(g2v0sin)=g2v02cossin=gv02sin(2)