How Long Until the Arrow Hits the Rock in Helm's Deep?

[LeHotDoge]

Homework Statement

Picture yourself in the castle of Helm's Deep from the Lord of the Rings. You are on top of the castle wall and are dropping rocks on assorted monsters that are 19.10 m below you. Just when you release a rock, an archer located exactly below you shoots an arrow straight up toward you with an initial velocity of 45.0 m/s. The arrow hits the rock in midair. How long after you release the rock does this happen?

Homework Equations

delta x = volt + at^2

v=vo+at

v^2=vo^2+2a(delta x)[/B]

The Attempt at a Solution

the initial velocity of the rock is 0, the acceleration of the rock is -9.8 m/s^2, the total displacement is -19.10 m.
delta x = volt + at^2
-19.10 = 0 + (-9.8)(t)^2
1.948 = t^2
t for rock =1.395 s
the initial velocity of the arrow is 45 m/s, the total displacement is 19.10m, and the acceleration is -9.8m/s^2
delta x = volt + at^2
19.10 = (45)(t) + at^2
19.10-45t=at^2
19.10-45=at
-25.9=(-9.8)(t)
2.642=t for arrow
t for arrow - t for rock = amount of time before they meet
2.642 s - 1.395 s = 1.247s

 

[Orodruin]

No, you cannot do it this way. The rock will not fall all the way before hitting the arrow and the arrow will not go all the way up before hitting the rock. Furthermore, the times they both take from being released until hitting each other must be the same, since they are released simultaneously and hit each other simultaneously.

In addition, your arithmetic for the solutions is also wrong. In particular that for the arrow:

19.10-45t=at^2
19.10-45=at

 

[LeHotDoge]

No, you cannot do it this way. The rock will not fall all the way before hitting the arrow and the arrow will not go all the way up before hitting the rock. Furthermore, the times they both take from being released until hitting each other must be the same, since they are released simultaneously and hit each other simultaneously.

In addition, your arithmetic for the solutions is also wrong. In particular that for the arrow:

Thank you for responding, I realize my solution is wrong, that is why I posted here.

 

[ehild]

1

Homework Equations

delta x = volt + at^2

The equation is wrong. Check.

 

[Orodruin]

Thank you for responding, I realize my solution is wrong, that is why I posted here.

So based on the comments you have received so far, how would you change it?

If you are looking for someone to give you a solution, this is not how we operate at Physics Forums. We believe it is much more effective learning if you do the problem yourself based on hints from helpers.