Kinematics Water shooting out of hose

[hanlon]

Homework Statement

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 above the ground. When you quickly turn off the nozzle, you hear the water striking the ground next to you for another 2.0 . find the water speed as it leaves the hose nozzel

Homework Equations

v = v_o + at
x = x_o + v_o*t + (1/2)at^2
v^2 = v_o^2 + 2a(x - x_o)
v_a = (v + v_o)/2

where v_o is initial velocity x_o is initial distance v_a is average velocity

The Attempt at a Solution

dunno if I can actually do this but I derived my own equation adding the top half (the parabola area) and the bottom the part equal 1.5m

top

0 = 2v_o + 19.6t ( v_o + at) for both 2 halfs of the parabola

bottom

-1.5 = v_o*t + 4.9t^2

add top and bottom

0 = v_o*t - 4.9t^2 +1.5 + 2v_o + 19.6t

simplify

-v_o = (-4.9t^2 + 19.6t +1.5)/ (t+2)

solve for v_o with t = 2

v_o = 5.275 m/s

I don't know if I was mathematically correct to add those equations together, can anyone help please

Thank You.

 

[CanIExplore]

Sorry hanlon but your work is hard to follow. Use the subscript and superscript buttons provided above the input text field when posting, and any other necessary formatting to make it easier to read. You've also written down equations with values already plugged in without specifying which of the relevant equations you've used. It's hard to see where those values came from.

top

0 = 2v_o + 19.6t ( v_o + at) for both 2 halfs of the parabola

bottom

-1.5 = v_o*t + 4.9t^2

Where does the value 19.6 come from? Also, can you tell me how you got those equations you're using? Are they derived from the relevant, constant acceleration equations?

 

[Redbelly98]

I, too, did not follow your derivation. Let's look at those equations again:

Homework Equations

v = v_o + at
x = x_o + v_o*t + (1/2)at^2
v^2 = v_o^2 + 2a(x - x_o)
v_a = (v + v_o)/2

where v_o is initial velocity x_o is initial distance v_a is average velocity

Let's make a list of all the quantities that appear here:

t
x
x0
v
v0
a​

(Since v_a is simply (x-x0)/t, I didn't bother listing it.)
Question for you: which of the quantities are given in the problem statement? Which quantity is being asked for? That information should help with choosing which equation (in your list above) will work out for this problem.