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 {\rm m} above the ground (see the figure ). When you quickly move the nozzle away from the vertical, you hear the water striking the ground next to you for another 2.2 s.
Actually, Steve should have used t = 1.1 s in his calculation. That is the amount of time the water spends coming down from maximum height.
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I assume you want to know how high the stream of water reached.
Well, you have so little information, the useful formulas are necessarily few. How about
s = 1/2 at2 ?
You have a and t, so plug 'em in to get s, the height
s = 4.9 (2.2)2 = 23.716m
That's some nozzle! 7 stories high!
s = v(i)t + (1/2)at²
-1.5 = 2.5 v(i) - 4.9 * 2.5²
v(i) = [4.9 * 2.5² - 1.5] / 2.5
v(i) = 11.65 m/s
The answer can't have more than 2 sig figs ... so the water speed as it leaves the nozzle is 12 m/s
To find the horizontal distance that the water stream traveled before hitting the ground, we can use the equation of motion for vertical motion. The equation is given by:
h = u*t + (1/2)*g*t^2
Where:
h = height of the object (1.5m in this case)
u = initial vertical velocity (0 m/s since the nozzle is pointed vertically upwards)
t = time taken for the object to reach the ground (unknown)
g = acceleration due to gravity (assumed to be 9.8 m/s^2)
Since we need to find the time (t) taken for the water stream to hit the ground, we rearrange the equation to solve for t:
t = sqrt((2h)/g)
Plugging in the values, we get:
t = sqrt((2*1.5)/9.8)
= sqrt(0.3061)
≈ 0.5538 s
So, the time taken for the water stream to hit the ground when the nozzle is pointed vertically upwards is approximately 0.5538 seconds.
Now, given that you hear the water striking the ground next to you for an additional 2.2 seconds, we can calculate the total time taken for the water stream to reach the ground after you moved the nozzle away from the vertical position.
Total time = Time taken for the water stream to hit the ground vertically + Additional time taken after moving the nozzle away
Total time = 0.5538 s + 2.2 s
= 2.7538 s
Therefore, the total time taken for the water stream to hit the ground after moving the nozzle away from the vertical position is approximately 2.7538 seconds.