Rocket; velocity and postion vectors

You will also have to integrate in two dimensions, so you will have two integration constants for both vx and vy. In summary, to find the velocity and position vectors as functions of time for a faulty model rocket, you must integrate the given acceleration components and use the given initial velocity and position values to determine the integration constants. You will need to integrate in both the x and y directions and have two integration constants for each.
  • #1
masterstakes
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Homework Statement


A faulty model rocket moves in the xy-plane. The rocket's acceleration has components: ax(t) = 2.5t² and ay(t) = 9 - 1.4t
At t= 0, the rocket is at the origin and has velocity V0 = 1i + 7j
(a) calculate the velocity and positions vectors as functions of time
(b) What is the max height rreached by the rocket?
(c) What is the horizontal displacement of the rocket when it returns to y = 0?

Homework Equations

The Attempt at a Solution


well, I am not sure where to start. :confused:
perhaps take the antiderivitives of the accelerations functions until you get time or velocity?
then plug in those answers to the velocity vector?
 
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  • #2
masterstakes said:

The Attempt at a Solution


well, I am not sure where to start. :confused:
perhaps take the antiderivitives of the accelerations functions until you get time or velocity?
then plug in those answers to the velocity vector?

You're correct that you have to integrate the acceleration functions to get the velocity and then displacement. However you don't quite "plug in those answers to the velocity vector," rather you are told v(t=0) and r(t=0). You will use those values to determine the integration constants.
 

FAQ: Rocket; velocity and postion vectors

What is a velocity vector?

A velocity vector is a mathematical representation of an object's speed and direction of motion. It is typically denoted by an arrow, with the length of the arrow representing the object's speed and the direction of the arrow representing the object's direction of motion.

How is a velocity vector different from a position vector?

A velocity vector represents an object's speed and direction of motion, while a position vector represents an object's location in space. Velocity vectors are used to describe an object's motion, while position vectors are used to describe an object's location.

What factors affect the velocity of a rocket?

The velocity of a rocket can be affected by various factors, including the amount of thrust generated by the rocket's engines, the mass of the rocket, and external forces such as air resistance and gravity.

Can the velocity vector of a rocket change during flight?

Yes, the velocity vector of a rocket can change during flight. As the rocket burns fuel and becomes lighter, its velocity may increase. Additionally, external forces such as air resistance and gravity can also affect the velocity of a rocket.

How are velocity and position vectors used in rocket trajectory calculations?

Velocity and position vectors are used in rocket trajectory calculations to predict the path of a rocket's flight. By considering the velocity and position of a rocket at different points in time, scientists and engineers can calculate the trajectory of the rocket and make adjustments to ensure it reaches its intended destination.

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