Rocket Challenge

A. For this challenge, our goal was to predict where our rocket would land when launched at a particular angle. The purpose was to test our skills in applying the formulas we had previously learned in the unit to see if we could accurately make a prediction. Unfortunately, no one in our class took a photo of the set up but the rocket resembled something like the picture below:

Basically, the rocket had a few components including an air pump, a wooden base used to launch the rocket with nails to hold it in the ground, the rocket, the wooden angle and the cap. We sued a special measuring deice to calculate how many meters the rocket flew.  The base was set at a particular position, the nails were put in place, the angle was placed underneath the launcher supporting a platform, and the air pump was attached to the base. The cap had to be firmly smashed onto the part that actually launched the rocket or else it wouldn't work. The angle we sued to make our prediction was 40 degrees.  After that the rocket was placed over top and we were ready to launch. 

B. After we set up the rocket as described above, we unfortunately only had time to run one (proper) trial due to time, but luckily, it was accurate and we were able to get the desired results. It took a few pumps to launch the rocket, but it eventually went but did not land snout down in the ground which was desired for more accurate results. We found the cap, reset the rocket, and did the same thing about 2 more times until the rocket finally landed in the ground and we were able to get an accurate measurement. We found data for displacement in the x and y direction,, velocity in the x and y directions when testing for both angles, time. As previously mentioned, we only ran one accurate trial, and the data table for the 40 degree angle is below. We ultimately wanted to make our prediction for the 25 degree angle.

  

Below are simply the values and 2 diagrams that calculated for visual purposes. How we actually came to these answers will be shown in the next step.

C.  Below are the empty diagrams from above showing what we needed to solve for: 

We started off solving for the velocity of the rocket because we knew that no matter what angle it was launched at, the velocity would stay the same. Below is a picture of the set up and the work. In order to calculate the velocity, we needed to find velocity in the x direction first. We used the formula, vx= change in x in the horizontal direction divided by the time. With that we got a velocity of 13.15 m/s.

 The next step was to solve for the hypotenuse which would be the actual velocity of the rocket. We used the cosine of 50 degrees and got a velocity of 20.46 m/s.

Now that we had the velocity we were able to move on to actually make the prediction for the 25 degrees. Once again we used a diagram to illustrate the situation. To ultimately solve for the distance the rocket would travel at 25 degrees, we would have to use the displacement formula, but in order to use that we need to solve for the velocity in the y direction. To do that we used the cosine of 25 degrees and came up with a viy of 18.54 m/s. 

With that, we moved on to the displacement formula to solve for the time. The displacement in the y direction is 0 because the rocket started and stopped at virtually the same place on the ground. The work is below and we came up with a time of 3.78 seconds.

Finally, to solve for displacement in the x direction with the 25 degree angle, we once again used the formula vx= change in x horizontally divided by time, but before that we had to find the velocity in the x direction by using the cosine of 65 degrees and came up with 8.64 m/s. We then plugged that in to the formula along with the time and got a prediction of 32.66m.

D. With our final prediction, our rocket ended up landing pretty close to our predicted value at 30.7 meters, well within the marking circle we created. Our percent error is shown below.