What Is the Acceleration Needed to Stop an Arrow?

[B18]

Homework Statement

An arrow is shot straight up in the air with an initial speed of 220 ft/s. If on striking the ground it embeds itself 8.00 in into the ground, find the magnitude of the acceleration (assumed constant) required to stop the arrow, in units of feet/second^2.

Homework Equations

4 basic kinematic equations.

The Attempt at a Solution

Does anyone see where I went wrong in my work?

 

[jackarms]

The problem is just that you're using constant acceleration over the entire distance from the top of its path down to when it's embedded in the ground, which you can't do since the acceleration changes once it's in the ground. There's some funky stuff in your equations for plugging in the initial and final velocities because of this. Try instead using the interval from when the arrow hits the ground to when it stops 8 in. later.

 

[B18]

Becomes a really easy problem when you know Vf=-Vi for velocities.

 

[CWatters]

or in other words.. if you throw something up in the air with velocity V it will hit the ground at the same velocity V. So you can forget that part of the problem and pretend the arrow was just fired at the ground.