Prove these statements: (a) As long as you can ignore the effects of the air, if you throw anything vertically upward, it will have the same speed when it returns to the release point as when it was released. (b) The time of flight will be twice the time it takes to get to its highest point.

Solution to 16DQ Consider a ball thrown upwards. Assuming that there is no air resistance, and are the initial and final velocities.Now, let us see what happens when the ball is moving upwards: Step 1 Here, at t=0, the ball would have a initial velocity and when it reaches the highest point t=t, the final velocity is 0. Considering the first equation of motion, Here v=0, thus Now using the third equation of motion, Step 2 Using the same equations from step 1 we get, [Note: distance of flight āsā is same for both upward and downward motion] Thus . Therefore it is proved that without air resistance both the velocities are same.