# How to find the initial velocity of a projectile, knowing only these?

1. Aug 14, 2014

### charlotteyip

Hi all,

I have been given a projectile motion problem, where a ball is launched from a catapult. The range, maximum height and the launching angle is known. The range is 2.32m, the max. height is 1.26m and the launching angle is 35° from the horizontal. The projectile flight goes for 1.125 seconds (that is, it is in the air for 1.125 seconds).

However, I need to find the initial velocity of the ball. How do I do this with the information given?

I have to do this (calculate all the relevant physical quantities) for a model that takes into consideration of drag (that is, a realistic model) and a model where gravity is the only real force acting on the projectile (an ideal projectile).

I am in Grade 11 AUS, so my knowledge of mechanics/physics is limited.

From a very confused student.

2. Aug 14, 2014

### Bandersnatch

Hi charlotteyip, welcome to PF!

You say your knowledge is limited. Tell us what you do actually know. Are you aware of kinematic equations. Have you tried applying them? If yes, what went wrong? If not, what makes it hard for you to do so?

The forum rules dictate that you show us your work before we can help you - that's what the pre-formatted three-part posts(that you've deleted) are for.

And I'd say forget about including drag - it'd require basic differential equations knowledge. Focus instead on the simplified model.

3. Aug 14, 2014

### charlotteyip

Oops, I am very sorry about that. I am aware of the 4 kinematic equations, however, won't using those only give me the average velocity instead of the instantaneous velocity? Perhaps I should explain the task in a better, more detailed way:

The task was to create a projectile launcher (I chose a catapult) that can launch a ball consistently. The launcher was then placed in front of a brick wall, and the width and height of a brick was measured. The ball was launched in front of the brick wall, and the entire process was filmed at 240fps (frames per second). Using purely this method, calculations and the recording, I am meant to find the relevant physical quantities such as; displacement (incl. x & y components), velocity (incl. x & y components), elastic potential energy (since a rubber band was used on the launcher), etc. etc.

My attempt at this task so far is like so:
Using the measurement from the backdrop, I've found the maximum height (1.26m) and the range (2.32m). From the recording, I also calculated from fps to seconds; and found that the flight time was 1.125 seconds. Using 2 rulers and a protractor, I've also found the launch angle which is 35° from the horizontal.

I know that I can continue using the backdrop to find the x & y components of displacement at any specific time by the measurement of bricks. And with the x & y components found, I can apply Pythagoras' Theorem to calculate the net displacement. So calculating the displacement is not a problem for me. Calculating the elastic potential energy also only requires simple laboratory work. However I am having trouble calculating the velocity, and my attempt has been like so:

I originally had thought that using the formula: velocity=displacement/time, I could easily find the velocity at any given time. However, my teacher has told me this formula only calculates the AVERAGE velocity at the given time. What I am required to do is to find the instantaneous velocity. However, he has told me that to find this, I must find the initial velocity of the ball first. I'm not sure what calculations I can perform to do so. I read on another forum that this formula should calculate the initial velocity: Range = v02sin2θ/g. But is this right? If so, how was this formula developed?

Sorry for the long paragraph, but thank you so much for your consideration!

4. Aug 14, 2014

### Bandersnatch

Alright, can you write down the full kinematic equation for displacement(separately for y and for x), and tell us which bits are constants, which are variables, which you think you already know and which are missing?
Try describing what each symbol represents, if you can.

5. Aug 14, 2014

### Staff: Mentor

Hi charlotteyip, Welcome to Physics Forums.

Your teacher is correct that displacement/time yields average velocity, and that for the more complicated motion of a projectile (which undergoes acceleration due to falling) it's not so useful.

HOWEVER! Projectile motion consists of two independent components: a vertical component and a horizontal component. Only the vertical component undergoes acceleration; the horizontal component is a nice constant velocity, so v = d/t works just fine for that component.

If you have one component of the launch velocity and the launch angle, Pythagoras will give you the other and the total velocity.

You actually have more than enough information to work with and there are several possible approaches you can use to find the initial velocity. You might investigate a few and compare results (accuracy and uncertainty in measurements will affect some quantities more than others). For example, above I've described using the horizontal component along with the known launch angle. You can also look at the vertical component: you know the maximum height that the projectile achieves so you can determine the vertical component of the launch speed (what is the speed of an object dropped from that height when it reaches the ground).

Yes, the range equation for a projectile launched on a level plane is $Range = \frac{V_o^2}{g} sin(2\theta)$. It's developed using the standard kinematic formulas. Starting with a given velocity and launch angle the vertical component is used to determine the total time of flight which is then plugged into the horizontal motion formula. A little trig-identity magic then yields the final form as given.

6. Aug 14, 2014

### charlotteyip

Ah I see! I completely forgot that v=d/t can still be used to calculate the horizontal component of the velocity! With that, I can calculate the initial velocity easily! Thankyou so much for your help!!

7. Aug 15, 2014

### dean barry

You are using time lapse photography ?
Mesuring distance travelled by the projectile between two frames is possible then ?
You can calculate the distance travelled after launch, this will be a good value for initial velocity.

velocity (m/s) = distance (m) / time (s)
velocity = ( distance travelled in 1 frame ) / ( 1 / 240 )

I know you are making straight lines from a curved path, but it wont be far away.