What is the water speed as it leaves the nozzle?

[hitemup]

Homework Statement

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Suppose you adjust your garden hose nozzle for a hard stream of water. You point the nozzle vertically upward at a height of 1.5 m above the ground. When you quickly turn off the nozzle, you hear the water striking the ground next to you for another 2.0 s.
What is the water speed as it leaves the nozzle?

Homework Equations

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v_avg = Δ_x/ Δ_t
v_final² =v_initial² + 2ax

The Attempt at a Solution

From the v_avg equation:
v_g = 1.5/2t + 10t
v₀ = 1.5/2t - 10t

From the other equation

http://www4a.wolframalpha.com/Calculate/MSP/MSP10431h9ic8g7736e702600003bb73a2eg362c825?MSPStoreType=image/gif&s=34&w=238.&h=35.

http://www4a.wolframalpha.com/Calculate/MSP/MSP38881h9ic4fc19b732c400004f1gdedhga6cgg3b?MSPStoreType=image/gif&s=34&w=38.&h=18.
http://www4a.wolframalpha.com/Calculate/MSP/MSP38851h9ic4fc19b732c400002b4de3h0dg0716h1?MSPStoreType=image/gif&s=34&w=49.&h=18.

v₀ was (1.5/2t - 10t).
So it becomes 0.75 - 10 = -9.25.

I think my answer is correct because I've come across the value of 9.25 on some other topics too. I'm not asking for a value correction. But what I found is minus 9.25 while others claim it is plus 9.25. Is this because of the direction of the water? Also, what about the spots I wrote (1-t). Have they simply become zero?

 

[haruspex]

You wrote 1.5/2t when you meant 1.5/(2t), then used it as though it wss (1.5/2)t. t cannot possibly be 1; look at the 1-t in your diagram.
There's a much quicker way. You have the time from the last drops of water leaving the pipe to hitting the ground, you have the acceleration, and you have the net change in height. One SUVAT equation will relate these to the initial velocity.

 

[hitemup]

You wrote 1.5/2t when you meant 1.5/(2t), then used it as though it wss (1.5/2)t. t cannot possibly be 1; look at the 1-t in your diagram.
There's a much quicker way. You have the time from the last drops of water leaving the pipe to hitting the ground, you have the acceleration, and you have the net change in height. One SUVAT equation will relate these to the initial velocity.

Thanks for pointing out the silly mistake. This, unfortunately, was the first way to come to my mind. I'd better think more. :D

 

[hitemup]

Okay now I've come up with t = 0.92s.
I'd be glad if you could look at it.
http://www.sketchtoy.com/63302148

 

[haruspex]

Okay now I've come up with t = 0.92s.
I'd be glad if you could look at it.
http://www.sketchtoy.com/63302148

To that many digits, yes.