A ball thrown vertically upward, returns to the thrower's hand. Which part of journey needs the longer time?

Question

**does the upward or the downward journey requires longer time?

Answer for (a) no air resistance, and (b) in the presence of air resistance.

Hint: the acceleration due to air resistance is always in a direction opposite to the motion

Answer 1

Depends upon the thrust and the vertical height achieved.

Upward     = Thrust - air resistance - gravity

Downward = gravity- air resistance

Generally, longer time in downward

Answer 2

with no air resistance, the times are the same (same absolute velocity when it leaves/enters the hand - the ball is under constant acceleration the whole time, and the path is symmetrical)

With air resistance, which is a function of velocity, we can know that it always works to slow down the ball, so that the (negative) acceleration on the way up is greater than the (positive) acceleration on the way down - i.e., it helps gravity on the way up, and hinders it on the way down, so it will be traveling more slowly on the way down, and hence will take longer.

Answer 3

(a) Without air resistance :

Same time for both journeys

(b) With air resistance :

During upward journey, force due to gravity and air resistance add up as both are downwards and against the motion, so deceleration is more and time will be more than in downard journey in which case force of gravity is in the downward direction and air resistance in the upward direction and acceleration is less than deceleration in the upward direction. So time in the downward direction is less.

Answer 4

downward takes longer, if terminal velocity is less than initial thrown velocity.

otherwise same time, air or no air.

Answer 5

Well, in no air, they would take the same exact time. With air resistance, I would say, just a guess, however, that it would take longer to go down. The friction due to air resistance going up would add to the constant gravity from earth (we are on Earth, right?). On the way down, however, the resistance would be going against the gravity.

Answer 6

The time it takes for the ball to go up is equal to the time for the call to go down to its original starting position