How Do Two Balls Dropped from a Window Hit the Ground Simultaneously?

[mike_302]

Homework Statement

A ball is thrown vertically upward from a window that is 3.6 m above the ground. Its initial speed is 2.8 m/s .

(a)with what speed does the ball hit hte ground?
(b)How long after the first ball is thrown, should a second ball be simply dropped from the same window, so that they both hit the ground at the same time?

Homework Equations

any of the 5 uniform acceleration equations. Gravity is -9.81 (he insists on the 1)

The Attempt at a Solution

I have (a) done... I obtained -8.86 m/s as the velocity when it hits the ground. But for (b), I don't know what method to go about doing this. My gut says there might be something easy, applying the "final speed" that I obtained in (a), but we also learned yesterday to do some graphing methods... Determine when two objects hit the same position, going at this velocity, and the other going at this velocity... That's what I'm trying to do here, but I can't figure it out.

For the dropped ball, the equation would be 0=1/2(-9.81)DeltaT^2 (from d2=v1DeltaT + 1/2aDeltaT^2 + d1 )

But what about the other ball?

 

[Delphi51]

The equation for the other ball would be the same except with a Vi*t term added.
Careful - the T's in the two equations are different. Better use t1 and t2 or something.
Solve each equation so you know t1 and t2. The difference is the answer!

 

[nlightner]

I would approach this problem by first understanding the concept of gravity and its effects on objects. Gravity is a force that pulls objects towards the center of the Earth and its strength is determined by the mass and distance between two objects. In this case, the two objects are the ball and the Earth.

To answer part (a), we can use the equation v2 = v1 + at, where v2 is the final velocity, v1 is the initial velocity, a is the acceleration due to gravity (-9.81 m/s^2), and t is the time. We know that the initial velocity is 2.8 m/s and the final velocity is 0 m/s (since the ball hits the ground), so we can rearrange the equation to solve for t:

t = -v1/a = -2.8/(-9.81) = 0.285 seconds

Therefore, the ball takes 0.285 seconds to hit the ground and its final velocity is -8.86 m/s.

For part (b), we can use the concept of free fall to determine when the second ball should be dropped so that both balls hit the ground at the same time. Free fall is when an object is only affected by the force of gravity, and in this case, both balls are in free fall.

To find the time it takes for the second ball to hit the ground, we can use the same equation as before, but this time the initial velocity is 0 m/s since the ball is being dropped. So, we have:

t = -v1/a = 0/(-9.81) = 0 seconds

This means that the second ball should be dropped immediately after the first ball is thrown in order for both to hit the ground at the same time. This is because both balls will experience the same acceleration due to gravity and will take the same amount of time to reach the ground.

In conclusion, as a scientist, I would use my understanding of gravity and the concept of free fall to solve this problem and provide a clear explanation for both parts (a) and (b).