3. Consider a projectile that is launched with initial speed V0 and angle :9. If you wanted to perform a dimensional analysis of this problem, you might start by guessing that the relevant physical quantities are: .7; horizontal position (m) 9 vertical position (In) V0 launch speed (m/s) 6 launch angle (rad) g acceleration due to gravity (m/sg) t time (s) (a) Apply the Buckingham Pi Theorem to show that in = git/VJ, 71'2 = 953/ 1/3, TF3 = gy/VOZ, and \"F4 2 5' represent a complete set of dimensionless quantities for this system. Note: The angular dimension for 6 is \"radians, \" which is already a dimensionless quantity. (1)) In class, we derived the following two equations describing the trajectory of a projectile launched from height h : 0: J; 2 (Va cos f9)t and y 2 (V0 sin 6)t ggtg. Rewrite each equation instead as a relationship among the dimensionless products in- from part (a)