Abb gun is discharged at a cardboard box of mass m2 = 0.65 kg on a frictionless surface. the bb has a mass of m1 = 0.012 kg and flys at a velocity of v1 = 99 m/s. it is observed that the box is moving at a velocity of v2 = 0.39 m/s after the bb passes through it.1. write an expression for the magnitude of the bb's velocity as it exits the box vf.2. what is the bb's final velocity vf, in meters per second?
3. if the bb doesn't exit the box, what will the velocity of the box v'2, be in meters per second?

Astudent throws a water balloon with speed v0 from a height h = 1.76 m at an angle θ = 21° above the horizontal toward a target on the ground. the target is located a horizontal distance d = 9.5 m from the student’s feet. assume that the balloon moves without air resistance. use a cartesian coordinate system with the origin at the balloon's initial position. (a) what is the position vector, rtarge t, that originates from the balloon's original position and terminates at the target? put this in terms of h and d, and represent it as a vector using i and j. (b) in terms of the variables in the problem, determine the time, t, after the launch it takes the balloon to reach the target. your answer should not include h. (c) create an expression for the balloon's vertical position as a function of time, y(t), in terms of t, vo, g, and θ. (d) determine the magnitude of the balloon's initial velocity, v0, in meters per second, by eliminating t from the previous two expressions.