An asteroid heads for Earth at 12 km/s. In addition, a NASA space team is able to attach a rocket booster to the asteroid, which then allows the asteroid to move at 28 degrees to its original path to a speed of 20km/s. What is its average accleration for acceleartion at (x) and acceleartion at(y).
For acceleration (x) I got 12.9 m/s^2,but I am not sure about that or acceleartion at (y). Any help would be greatly appreciated.
I may be missing something, but I don't see how you can compute an acceleration without knowing how long it takes to make the velocity vector change you mentioned. This would be the rocket "burn time" for example.
I see that you later "updated" the question with the burn time. It was then answered by BobPursley
To find the average acceleration of the asteroid in the x-direction (horizontal) and y-direction (vertical), we can use the following formulas:
1. Average acceleration (x) = (final velocity (x) - initial velocity (x)) / time
2. Average acceleration (y) = (final velocity (y) - initial velocity (y)) / time
First, let's break down the velocity components:
Initial velocity (x): 12 km/s (since the asteroid was initially moving at 12 km/s in the x-direction)
Initial velocity (y): 0 km/s (assuming no initial velocity in the y-direction)
Final velocity (x): To find the final velocity (x), we can use trigonometry. We know that the asteroid is now moving at 20 km/s at an angle of 28 degrees to its original path. So, the final velocity (x) can be calculated as follows:
Final velocity (x) = 20 km/s * cos(28 degrees)
Final velocity (y): To find the final velocity (y), we can also use trigonometry. The final velocity (y) can be calculated as follows:
Final velocity (y) = 20 km/s * sin(28 degrees)
Now, we can calculate the average accelerations:
Average acceleration (x) = (Final velocity (x) - Initial velocity (x)) / time
Average acceleration (y) = (Final velocity (y) - Initial velocity (y)) / time
The provided information doesn't include the time over which the rocket booster was attached, so we cannot determine the actual average acceleration values without this time value. If you have the time, you can substitute it into the formulas above and calculate the average accelerations in the x and y directions.