Lab 2 Kinematics PHY250L " ramp . Record your answer in variables ( you will calculate the velocity with magnitudes when you perform the experiment ) . " 2 . " Use the kinematic equations to derive a general equation for the time it takes a ball dropped from rest at vertical height , h , to reach the ground . Use this to write a general equation for the distance travelled by a projectile that is rolling off a table of height , h , with a horizontal speed of V . " 3 . " Prove that launching a projectile at 45 provides the largest range . Write the range as a function of . Take the derivative of the range with respect to and find the maximum angle . " 4 . " A butterfly flies along with a velocity vector given by v = ( a-bt ) ( ct ) where a = 1.4 m/s , b= 6.2 m / s , and c = 2.2 m / s . When t= 0 seconds , the butterfly is located at the origin . Calculate the butterfly 's position vector and acceleration