2D Motion with a missle/engines

[wallace13]

On a spacecraft two engines fire for a time of 505 s. One gives the craft an acceleration in the x direction of ax = 5.10 m/s2, while the other produces an acceleration in the y direction of ay = 7.30 m/s2. At the end of the firing period, the craft has velocity components of vx = 3610 m/s and vy = 4928 m/s. Find the magnitude and direction of the initial velocity. Express the direction as an angle with respect to the +x axis.



Vf= Vi +at

tan O= opp/adj

3610 m/s = Vi + (5.1 x 505)

Vi= 1034.5 m/s

tan O= 7.3/ 5.1
O= 55.06 degrees


the answer was incorrrect and I have no idea what else to do

 

[Kurdt]

You found the initial x component well enough but you didn't find the y component. You then need to find the magnitude (i.e. pythagoras) and then apply your tan formula to the initial speeds.

 

[baba89]

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I would first check the calculations and equations used to solve this problem. It is important to double check all the values and units used in the calculations to ensure accuracy. Additionally, I would consider the assumptions made in the problem, such as assuming constant acceleration and no external forces acting on the spacecraft.

If the calculations and assumptions were correct, then I would suggest using vector addition to solve for the initial velocity. The initial velocity vector can be represented as the sum of the two velocity components in the x and y directions, which can be calculated using the given acceleration values and time period.

Once the initial velocity vector is calculated, the magnitude and direction can be determined using trigonometric functions. The magnitude can be found using the Pythagorean theorem and the direction can be determined using the inverse tangent function.

It is also important to note that the direction of the initial velocity with respect to the +x axis may differ from the direction of the final velocity. This could be due to the spacecraft's trajectory and the angle at which the engines were fired, which may have resulted in a change in direction during the firing period.

In conclusion, as a scientist, I would suggest rechecking the calculations and assumptions made and using vector addition to accurately determine the magnitude and direction of the initial velocity in this scenario.