Calculate The Speed Of Nerf Dart With Pen-Paper Only.......

"Previous week we discussed about one of the important invention in the world of telecommunication-Optical Fiber. This week we will learn to calculate the speed of a Nerf dart(any) using pure physics.

NOTE: This article is not in any way an AFFILIATE or PROMOTES the purchase of Nerf products. Also this experiment can be done using other TOY gun "

Recently I had a random thought of calculating the speed of my Nerf Dart. So like others I googled about it. No result. Surely there were many great articles about it, but all of them required the use of another device which can be used to obtain the result. I didn’t have any interest of purchasing a costly device for just finding the speed of my NERF DART( I would better go and get some cheesed pizza for myself).

People might think Physics as one of those unnecessary  subjects which has nothing to do with day-to-day life. But NO, think again. A lot of exciting experiments can be conducted basing upon the laws of physics. When I didn’t find anything in particular in the internet, I thought of finding a way myself. This article involves the use of basic formula of physics i.e. V=U+AT where V is the final velocity, U is initial velocity(which represents the speed of the dart when released) and A is gravity while T is time. Load your Gun and let's get started.

Calculating the speed of the dart:-

Requirements:

Nerf Gun

Pen

Paper

Timer/Stopwatch/Any time measuring application

Experiment 1:

First things first. This experiment must be conducted outdoors and the weather must be wind-free. You might require an additional help (maybe call a friend) for perfect results, though I did it myself. Refer the above image.

Step 1:  Load your gun. Ready the stopwatch (or any other time measuring application). Point the gun towards the sky(watch out for birds) perpendicular to the ground.

Step 2: Now shoot the gun while switching on the timer. NOTE: The Timer must be switched on as soon as the dart is shoot. An additional help as mentioned above might help in this step.

Step 3: Stop the timer as soon as the dart hits the ground. No time delay must be made in this step too. Note the time taken by the dart to go up and down. I got a time of 2.8seconds. It may vary depending upon the accuracy of the experiment and power of the gun.

Step 4: You may find the speed of your dart in this step itself. Just multiply the time period obtained with 9.8 and then divide by two.

i.e. Suppose your time period as x, then…

    x/2 × 9.8

For instance in my case, my time period was 2.8, then…

    2.8/2 × 9.8 = 13.72 

Hence, my dart when released from the gun travels at the speed of 13.72m/s.

If you are not interested in the physics involved in this experiment you may stop here. If you are interested in this simple formula, read on…….

Experiment 2:

As mentioned earlier, in this article we use the physics formula v=u+at. When the dart is shot upward, gravity pulls it down. This force is represented by ''a'' in the formula. As it acts opposite to the force given by the gun, it is negative. The time period we recorded is the time taken by the dart to go up and come down. So, we need to divide it by 2 to obtain the time taken to reach the highest point upwards i.e. final velocity. When the dart reaches its maximum position the final velocity i.e. v becomes 0. This is because at this position the dart starts to move downwards. Initial velocity represented by u is the speed of the dart when it launches from the bust of the gun. Thus, u is unknown to us. Let us observe the equation now…..

Suppose x is your time period.

v = u + at

0m/s = u + (-9.8m/s × x/2)

Transpose the equation from right hand to left hand side……

-(-9.8m/s × x/2) + 0m/s = u

Hence…

9.8m/s × x/2 = u

This is the formula mentioned in step 4.

There is another, more accurate way to test the speed of the dart when launched by the gun. This procedure requires an additional setting. In this procedure we use the formula s=ut+(1/2)*at2.

Here the dart must be shot from a height towards the surface. Shooting the dart from a building is a good idea. Measure the height of your position i.e. the distance from the ground to your position. Shoot the dart down towards the surface perpendicularly. Record the time taken by the dart to hit the ground. Now input the same data in the above formula.

Let's assume the distance as ''h'' and time as ''t'', then….

s=ut+1/2×at² 

     

Input the data………

h=ut+1/2×9.8×t²

Transpose…..

-ut=-h+4.9t²

-u=(-h+4.9t²)/t

I personally didn’t test the second method yet. It gives a much more accurate result as it reduces the air resistance.

"NOTE: Take safety measures while performing the experiment. Avoid shooting at any individual while shooting downwards or hurting yourself. Always use Styrofoam Nerf darts to prevent complications. I won't be responsible for any damages."

There may be certain variations in the result due to accuracy and air resistance. A difference of 0.5 or 1m/s may occur in the result. This experiment helps us to understand the two major laws of motion and derive the speed of the Nerf dart when shot from the gun.

Hope you guys like the article. Next article under this section- Study of Car Engines

"All images and data are produced by me"