# Homework Help: Finding an equation of motion

1. Mar 14, 2013

### Deimantas

1. The problem statement, all variables and given/known data

From a height of 18 meters above ground, an object is thrown vertically upwards at a speed of 30m/s. Find the equation where height h depends on time t. Find the maximum height of the object.

2. Relevant equations

h=h0+v0t-(gt^2)/2

3. The attempt at a solution

The equation of motion of an object thrown vertically upwards is h=h0+v0t-(gt^2)/2
By inserting h0=18 and v0=30 we get
$h=18+30t-(gt^2)/2$, which is the correct answer. When t=3, h is max at 63.
Now my problem here is that instead of finding the aforementioned equation of motion in a book, i was supposed to create it myself, using differential equation methods. How?

Last edited: Mar 14, 2013
2. Mar 14, 2013

### HallsofIvy

Once the ball have been thrown up it has accelration -g, due to gravity. Acceleration is the derivative of velocity and velocity is the derivative of distance (height here).

So your differential equations problem is $d^2h/dt^2= -g$ with initial values h(0)= 18, h'(0)= v(0)= 30.

3. Mar 14, 2013

### Dick

You want to start from using that the derivative of the velocity is equal to the acceleration. So v'(t)=(-g). Integrate both sides to get v(t). Determine the constant of integration. Then v(t)=h'(t), so integrate again to get h(t)

4. Mar 14, 2013

### Deimantas

Thanks for helping me out :)