From the top of a tall building, you throw one ball straight up with speed v0 and one ball straight down with speed v0. (a) Which ball has the greater speed when it reaches the ground? (b) Which ball gets to the ground first? (c) Which ball has a greater displacement when it reaches the ground? (d) Which ball has traveled the greater distance when it hits the ground?

Solution 19DQ (a).The ball which one has thrown up is travelling faster.because it will going to travel until the velocity is zero at which point it will fall a greater distance than that of the ball initially thrown below. (b).Consider a ball thrown straight with velocity v.it has kinetic energy 1/2 mv .it goes upto some distance and return back to the point where it was thrown. When it returns to that point,it has same amount of kinetic energy so speed will same but in opposite direction to the ball was thrown down.so they both hit the ground in same time. (c). one ball straight down with speed v 0has greater displacement. (d).Remember the first ball to be thrown is always to be a greater speed compared to the second ball as it would have more time to accelerate,so distance between will always getting larger.the ball straight up with speed v ,will traveled the greater distance when it 0 hits the ground. Remember the first ball to be thrown will always be travelling at a greater speed compared to the second ball as it would of had more time to accelerate, so the distance between the two is always getting larger. Reference https://www.physicsforums.com/threads/question-which-one-travels-faster.5159/