Linear Motion Homework Problem

[_Pistolkisses]

Homework Statement

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

Homework Equations

I'm guessing, d = v2t-(0.5)at^2
and v1^2= (v2^2)-2ad.

The Attempt at a Solution

I subbed in v2=0, a = -9.8, and t= 2.0 in the first equation to get distance.

And then subtracted 1.5 from the distance and used the new distance in the second equation (v1^2= v2^2 -2ad) to find velocity and came up with 18.84m/s.

It's not right because I had no idea which distance to use or how to find the right distance because the time value of 2.0 seconds is confusing me (the wording, anyways).

Should distance be -1.5m instead? :S

 

[Shooting Star]

Should distance be -1.5m instead? :S

That's right. The water which leaves the nozzle with a speed of vi upward takes 2 secs to fall -1.5 m from the starting point, if up is taken as positive. Be careful about the signs of the other quantities.

 

[Moetasim]

I would suggest using the equation d = v1t + (0.5)at^2 to calculate the distance, where d is the distance, v1 is the initial velocity (in this case, 0 m/s), t is the time (2.0 s), and a is the acceleration due to gravity (-9.8 m/s^2). This will give you the distance from the nozzle to the ground, which should be 5.8 m.

Then, using this distance, you can use the equation v2^2 = v1^2 + 2ad to solve for the final velocity (v2). Substituting in v1 = 0 m/s, a = -9.8 m/s^2, and d = 5.8 m, you would get a final velocity of 18.84 m/s, which is the same result you got.

To answer the question about which distance to use, it would be the distance from the nozzle to the ground, which would be 5.8 m. This distance represents the height at which the water leaves the nozzle and begins to fall due to gravity. Therefore, it is the distance at which you would use to calculate the final velocity.

I hope this explanation helps and clarifies any confusion. Keep up the good work with your homework problems!