Projectile Motion: Time and Impact Velocity Comparison - Homework Question

[phizics09]

Homework Statement

When you toss a ball up and let it drop to the ground, compared to when you just let it fall, will the time it takes to reach the ground and impact velocity be equal?

Homework Equations

The Attempt at a Solution

For the time, they shouldn't be equal, since the height from which the ball starts falling is different right? But how come when you solve projectile motion problems with an original velocity in the vertical direction, you don't need to calculate the separate two paths--one up and one down--separately, but you still get the same answer?

 

[technician]

An assumption (physics is full of 'good' assumptions) is that air resistance can be ignored.
This is good in the first instance but it is obviously untrue and must be taken into account in a full analysis. But, you have to start some where

 

[phizics09]

What do you mean?

 

[CanIExplore]

Think about the two trajectories. In the case where the ball is thrown straight up, it will eventually reach a highest point at which its height from the ground is h. What is the velocity of the ball at that point? How is the similar or different to the velocity of the ball if you were to simply drop it from that same height?

 

[technician]

If there is no air resistance then there will be no difference at all

 

[gordonj005]

If there is no air resistance then there will be no difference at all

Now if you throw in air resistance, and assume the balls are identical, think about what would happen to the times then.