12.3.10 Evaluate /2 [(a cost)i + (a sin t)+ +k] dt 12.3.11 Find (t) that satisfies the initial condition 7' (t) = 4et + 3e, r(0) = 21 12.3.12 Find r(t) that satisfies the initial condition 7' (t) = = 12 +2 +k, 7(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 a measured from the horizontal if it just barely cleared a wall at a distance d feet from the origin and h feet high. 1 1:34 AM Tue Sep 20 The maximum height is the vertical component of the position vector at t = Vo sin a 2 1 (Sina)* + Vo sin a (o sina) = v sin a H = 2g Tflight = R= Vo cos a 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. 2v sin a g ... v sin(2a) 9 1 v sin a v sin a + 2 g g = Find the formula for the range of a projectile 2vo sin a The range or maximum distance is the horizontal component of the position vector at t = 2v cos a sin a v sin(2a) 9 (2vo sin av g = g g = Maximum Height Flight Time 9 1 v sin a 2 g Maximum Range 37 of 127 @ 20%