AP Physics question?

Question

A rock is thrown nearly straight upward from the edge of the top of a building at an initial speed of 16.0 m/s. Its trajectory will take it just past the edge, so that it lands on the ground. How much later must a second rock be dropped from rest at the same initial height of 14.1 m so that the two rocks hit the ground at the same time?

I've gotten this far:

The second rock will take 1.7sec after it is dropped to hit the ground

The first rock will reach its maximum height at 13.06m after 1.632sec

But how do I make this all come together?

Answer 1

Yes, you know that your first rock will hit 0 speed at the high point of its arc, so from that point it is just like you are dropping it from a slightly higher building.

Also, when the first rock falls back down to you, when it reachs you, it is now going the same speed DOWN as it was initially going UP when you first threw it.

so really, you can think of your ultimate experience with the first rock as if you were throwing it straight down at 16 m/s from the top of the same roof where you are simply dropping the second rock.

Since gravity affects both rocks equally, the first rock's portion of the downward journey (from the rooftop itself) is shorter by exactly the initial velocity.  which for a 14.1 meter roof, and a 16 m/s speed, means ,881 seconds (the first rock would hit the ground .881 seconds faster, if it were hurled straigh down at the same time the second rock were simply dropped.

So then we add your 1.632 seconds required for the first rock to actually get to that point (back to the roof line with a downward speed of 16 m/s

and we get 2.51S for the total time the first rock must be thrown up before the second rock is released.

Answer 2

find the time it takes for the first rock to hit the ground.

first, use the equation v^2 = vi^2 + 2a(delta x)

use vi (v initial) = 16 m/s a= 9.81 delta x = 2(14.1)

find the vfinal.

use that value to find the time using this equation

v = vi + at

solve for time . and subtract your two times.

hope that helps