## Homework Statement

An arrow is shot vertically upward with an initial speed of 25 m/s. Two seconds later, another arrow is shot upward with the same speed. On its way up, the second arrow meets the first arrow on its way down. Assume that both arrows experience a constant downward acceleration of 9.8 m/s2.

How long does it take (from the time the first arrow is shot) for the arrows to meet?

## Homework Equations

d = vf * t - 0.5(a)(t)2
tA1 = tA2 + 2

## The Attempt at a Solution

dA1 = 25t - 4.9t2
dA2 = 25t - 4.9t2

Since dA1 = dA2

25tA1 - 4.9tA12 = 25tA2 - 4.9tA22

Since tA1 = tA2 + 2

25(tA2 + 2) - 4.9(tA2 + 2)2 = 25tA2 - 4.9tA22

19.6t = 50-19.6
t = 1.55 s

The correct answer is 3.55 s

berkeman
Mentor

## Homework Statement

An arrow is shot vertically upward with an initial speed of 25 m/s. Two seconds later, another arrow is shot upward with the same speed. On its way up, the second arrow meets the first arrow on its way down. Assume that both arrows experience a constant downward acceleration of 9.8 m/s2.

How long does it take (from the time the first arrow is shot) for the arrows to meet?

## Homework Equations

d = vf * t - 0.5(a)(t)2
tA1 = tA2 + 2

## The Attempt at a Solution

dA1 = 25t - 4.9t2
dA2 = 25t - 4.9t2

Since dA1 = dA2

25tA1 - 4.9tA12 = 25tA2 - 4.9tA22

Since tA1 = tA2 + 2

25(tA2 + 2) - 4.9(tA2 + 2)2 = 25tA2 - 4.9tA22

19.6t = 50-19.6
t = 1.55 s

The correct answer is 3.55 s

I believe it's just that you have this equation off: tA1 = tA2 + 2

The 2nd arrow is shot 2 seconds after the first, not the other way around. Does that fix it?

berkeman
Mentor
I believe it's just that you have this equation off: tA1 = tA2 + 2

The 2nd arrow is shot 2 seconds after the first, not the other way around. Does that fix it?

Actually, the only error is related to that equation. You forgot to add the 2 seconds to the time of the 2nd arrow being shot. You solved tor t2, and they asked for t1.

I tried switching them around, but I still ended up with 1.55 s, help?

berkeman
Mentor
I tried switching them around, but I still ended up with 1.55 s, help?

berkeman
Mentor