How Do You Calculate the Constants A and C for a Rocket's Trajectory Equation?

Click For Summary
SUMMARY

The discussion focuses on calculating the constants A and C in the trajectory equations of a rocket launched from a height of 50.0 meters. The position coordinates are defined as x(t)=A+Bt^2 and y(t)=C+Dt^3, with known constants B=2.00 m/s² and D=0.500 m/s³ derived from the acceleration vector a=(4.00i+3.00j) m/s² at t=1.00s. The initial height of the rocket indicates that C must equal 50.0 meters, representing the starting vertical position. The value of A remains to be determined based on the horizontal position at t=0.

PREREQUISITES
  • Understanding of kinematic equations in physics
  • Knowledge of derivatives and their application in motion analysis
  • Familiarity with vector notation and acceleration components
  • Basic principles of projectile motion
NEXT STEPS
  • Calculate the initial horizontal position A using the trajectory equation
  • Explore the implications of different launch angles on trajectory equations
  • Study the effects of varying constants B and D on rocket motion
  • Learn about numerical methods for solving differential equations in motion analysis
USEFUL FOR

Students and professionals in physics, aerospace engineering, and anyone interested in understanding the dynamics of rocket trajectories and motion equations.

azn4lyf89
Messages
17
Reaction score
0
A rocket is fired at an angle from the top of a tower of height 50.0m. Because of the designs of its engines, its position coordinates are of the form x(t)=A+Bt^2 and y(t)=C+Dt^3, where A, B, C, and D are constants. The acceleration of the rocket after 1.00s after firing is a= (4.00i+3.00j)m/s^2. Find the constants A, B, C, and D including their SI units.

I took the derivative of the position vectors twice to get the acceleration vector and plugged in 1.00s into t to find D=0.500m/s^3 and B=2.00m/s^2. I am stuck on where to go after that to get A and C.
 
Physics news on Phys.org
azn4lyf89 said:
A rocket is fired at an angle from the top of a tower of height 50.0m. Because of the designs of its engines, its position coordinates are of the form x(t)=A+Bt^2 and y(t)=C+Dt^3, where A, B, C, and D are constants. The acceleration of the rocket after 1.00s after firing is a= (4.00i+3.00j)m/s^2. Find the constants A, B, C, and D including their SI units.

I took the derivative of the position vectors twice to get the acceleration vector and plugged in 1.00s into t to find D=0.500m/s^3 and B=2.00m/s^2. I am stuck on where to go after that to get A and C.

What is C. Wasn't it given to you? What is A then? Remember the equation describes position. Where was its initial position?
 

Similar threads

Constant acceleration in a rocket
  • · Replies 4 ·
Replies
4
Views
2K
Finding shortest distance between an observer and a moving object
  • · Replies 13 ·
Replies
13
Views
2K
How to calculate velocity of infinite-stage rocket?
  • · Replies 2 ·
Replies
2
Views
1K
Determine when (m), and how long the rocket should fire.
  • · Replies 2 ·
Replies
2
Views
2K
Upward and downward movement of a rocket with the equation of motion
  • · Replies 13 ·
Replies
13
Views
2K
Model Rocket Launch: Maximum Height, Time, and Duration Calculations
  • · Replies 1 ·
Replies
1
Views
2K
How Does the Relativistic Rocket Equation Describe Velocity?
  • · Replies 2 ·
Replies
2
Views
2K
Forces - Space Shuttle Takeoff Calculations
  • · Replies 22 ·
Replies
22
Views
3K
Hitting a rocket with a projectile
  • · Replies 53 ·
2
Replies
53
Views
5K
How to Calculate Amplitude Decrease in Damped Harmonic Motion After 10 Cycles?
  • · Replies 3 ·
Replies
3
Views
986