# Kinematics - projectile motion - time to maximum height?

Kinematics -- projectile motion -- time to maximum height?

## Homework Statement

The nozzle of a fire hose discharges water at a speed of 10 m/s. The nozzle is aimed straight up. How long does it take for a water drop to reach its maximum height?
vi= 10 m/s
vf= 0 m/s
t=? s
a= -9.8 m/s^2
delta−x= ?

## The Attempt at a Solution

OK, so I'm assuming that solving this takes 2 steps. One entails finding the maximum height, then using a kinematic formula to find time. Is that logic sound?

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ehild
Homework Helper
What are the relevant equations?

ehild

I tried this:
Vfy=Viy+Ay*t
0 m/s=10 m/s-9.8 m/s^2*t
-10 m/s=-9.8 m/s^2 *t
t=10 m/s / -9.8 m/s^2
t=1.02 s

ehild
Homework Helper
It is correct. You see, the maximum height was not needed.

ehild

1.02 s is not an option for this multiple choice problem, the closest is 1.0 s. Is that likely the answer then?

Edit: The question asks how long it takes to reach maximum height, so because it is a parabola, it stands to reason that 1.02s/2=0.51s is how long it takes to reach the maximum height. Right?

ehild
Homework Helper
The data in the problem are given with two significant digits. Round of your result to t=1.0 s. .

What is parabola?

When does a body projected straight upward reach maximum height? What is its velocity at the apex?
What is the maximum height?

What would be the velocity at t=0.5 s? Would the water drop move upward or downward then? Does it reach the maximum height at t=0.5 s?

ehild

I don't know. I remember someone in class saying that projectile motion was a parabola...

t=1.0 s means what? The time it takes for the motion to finish? or the time at which the water reaches its maximum height?

ehild
Homework Helper
The motion is not parabola. A graph of a function can be parabola.

You applied the equation Vfy=Viy+Ay*t. What do the letters mean? You substituted Vfy=0. If you throw up a pebble, will it reach the ground with zero velocity? Where is the velocity zero?
Just throw up something and see...

ehild

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