How Do You Calculate Initial Velocity and Angle in Two-Dimensional Kinematics?

[zn23]

Homework Statement

Useful background for this problem can be found in Multiple-Concept Example 2. On a spacecraft two engines fire for a time of 871 s. One gives the craft an acceleration in the x direction of ax = 6.00 m/s2, while the other produces an acceleration in the y direction of ay = 5.68 m/s2. At the end of the firing period, the craft has velocity components of vx = 5800 m/s and vy = 6420 m/s. Find (a) the magnitude and (b) the direction of the initial velocity. Express the direction as an angle with respect to the +x axis.

Homework Equations

most likely the use of the 4 main kinematics equations

v2=v1+at
v2^2=v1^2+2ad
x=1/2(v1+v2)t
x=v1t+1/2at^2

The Attempt at a Solution

basically i have no idea where to begin in this question, its computer question and I keep getting the incorrect answer, if anybody has suggestions how to begin this problem that would be nice, like what wud i do with that time of 871 s?

 

[tiny-tim]

most likely the use of the 4 main kinematics equations

v2=v1+at
v2^2=v1^2+2ad
x=1/2(v1+v2)t
x=v1t+1/2at^2

Hi zn23!

You can forget equations involving x … there's no distance involved in this problem.

Hint: Find ∆Vx and ∆Vy, and then its' a simple vector addition problem .

 

[baba89]

I would approach this problem by first identifying the given information and the unknowns. From the problem statement, it is clear that we are dealing with kinematics in 2 dimensions, specifically the motion of a spacecraft with two engines firing for a given time period. The known values are the acceleration components in the x and y directions, the final velocity components, and the time of 871 seconds. The unknowns are the magnitude and direction of the initial velocity.

The next step would be to use the given equations and manipulate them to solve for the unknowns. For example, we can use the first equation, v2=v1+at, to solve for the initial velocity components in the x and y directions. We know the final velocity components, so we can plug those in along with the given accelerations and time to solve for the initial velocity components.

To find the magnitude of the initial velocity, we can use the equation v = √(vx^2 + vy^2). And to find the direction, we can use the equation tanθ = vy/vx, where θ is the angle with respect to the +x axis.

It is important to carefully consider the units and make sure they are consistent throughout the calculations. Additionally, double check the calculations to ensure they are correct.

Overall, the key to solving this problem is to clearly identify the given information and unknowns, and then use the appropriate equations to solve for them. It may also be helpful to draw a diagram and visualize the motion of the spacecraft to better understand the problem.