# Why are there two answers to (b)?

1. Oct 11, 2014

### hitemup

1. The problem statement, all variables and given/known data

A stone is thrown vertically upward with a speed of 24.0 m/s.

a) How fast is it moving when it reaches a height of 13.0 m/s?
b) How much time is required to reach this height?
c) Why are there two answers to (b)?

2. Relevant equations

x = v0t +- 1/2 at2

3. The attempt at a solution

I had no problem with the first two, but I've thought I need an explanation for the third one. Here is the graph and solutions. Does the second root appear because of the stone's falling right after reaching its maximum height?

http://www4c.wolframalpha.com/Calculate/MSP/MSP42811iec8be4feb3fd0e00001afd1ed1gd449fc6?MSPStoreType=image/gif&s=16&w=86.&h=18. [Broken] http://www4c.wolframalpha.com/Calculate/MSP/MSP42841iec8be4feb3fd0e00003d457bh4d7i14gi8?MSPStoreType=image/gif&s=16&w=78.&h=18. [Broken]
http://www4c.wolframalpha.com/Calculate/MSP/MSP42881iec8be4feb3fd0e0000509big5995b3732e?MSPStoreType=image/gif&s=16&w=392.&h=192.&cdf=Coordinates&cdf=Tooltips [Broken]

Last edited by a moderator: May 7, 2017
2. Oct 11, 2014

### Staff: Mentor

That's right. What goes up must come down!

It passes the 13m level twice. In fact, it passes through every level twice, except for the point at the very apex of the trajectory.

3. Oct 11, 2014

### phinds

Unless it exceeds escape velocity :D