Trigonometry and Potatoes!
This is a post to go into further depth of the launch Steven, Brandon, Dustin, and I did with the potato accelerator. The data that we collected from one of the three trials showed that the total distance of the launch was 535 ft, the total time it took the potato to hit the ground from the initial launch was 7.13 seconds, the angle of elevation was 40 degrees, and the observed height was 5′ 6″.
In order to find the peak of the potato in the launch we used two different methods. The first method was with the h=½(g)t² equation. So first we divided the total time by two in order to get how long it took from the peak of the launch to impact (3.565 sec.). We then plugged that number into the equation along with the acceleration due to gravity (9.81 m/s²) and were able to approximate that the height of the peak was 62.339 m. or 204.524 ft.
After we found the height of the peak by using that equation we decided to find the height with trigonometry. In order to do this we had to find the distance from launch to peak and the angle of elevation from the observer’s eye (Steven). To find the distance from launch to peak we just divided the total distance by two and came up with 267.5 ft. Our observed angle of elevation came out to be 40 degrees in this trial. Now that we had all our data we were able to figure out that we would have to use tangent to find the height. So since we knew the angle of elevation and the distance from launch to peak, we were able to determine that our equation would be tan(40)=x/267.5. To solve for x we transposed 267.5 over and got x=tan(40)267.5, we then realized that we had to add in Steven’s height (only up to his eye) so our official equation was x=tan(40)267.5+5.5. We then solved for x and our height of the peak came out to be 229.959 ft.
Now that we had found the height of the peak using two different methods we were able to compare the numbers. From the first method we got 204.524 ft. for the height and from the second method we got 229.959 ft. for the height. So in conclusion the theoretical equation h=½(g)t² turned out to be reliable in finding the height of the peak of the potato in the launch.