Model Rocket Motion Analysis: Reflecting on Time, Acceleration, Height, and Speed
How much time does it take for the rocket to reach a height of 4.2 m?
a) [tex]t=0.311 s[/tex]
What was the magnitude of the rocket's acceleration?
b) [tex]a=86.847 m/s^{2}[/tex]
Find the height of the rocket 0.20 s after launch.
c) [tex]y=1.736 m[/tex]
Find the speed of the rocket 0.20 s after launch.
d) [tex]V=17.369 m/s[/tex]
For this situation, we will use equations involving time, acceleration, height, and speed of the model rocket.
To determine the time taken for the rocket to reach a height of 4.2 m, we first calculate the average velocity of the rocket using the given speed. Then, by dividing the height by the average velocity, we find t = 0.311 s, as shown in equation (7).
Next, to find the magnitude of the rocket's acceleration, we utilize the equation y = 0.5at^2 with the known height reached and time taken, resulting in a = 86.847 m/s^2, as calculated in equation (10).
After that, to determine the height of the rocket 0.20 s after launch, we apply the same equation but substitute the time value, leading to y = 1.736 m, as obtained in equation (12).
Lastly, to find the speed of the rocket 0.20 s after launch, we use the equation V = at considering the rocket started from rest, giving V = 17.369 m/s, as computed in equation (15).
Reflecting on these calculations, we can comprehend the intricate interplay of time, acceleration, height, and speed in the motion analysis of a model rocket, offering insights into its dynamic behavior throughout its flight trajectory.