You're heading an international effort to save Earth from an asteroid heading toward us at 11km/s . Your team mounts a rocket on the asteroid and fires it for 10 min, after which the asteroid is moving at 21km/s at 32∘ to its original path.
In a news conference, what do you report for the acceleration imparted to the asteroid?
Express your answers using two significant figures separated by a comma. Assume that the positive x axis is in the direction of the initial motion of asteroid and y axis is perpendicular to it.
To find the acceleration imparted to the asteroid, we can use the formula for acceleration:
acceleration (a) = change in velocity (Δv) / time taken (Δt)
Given that the asteroid's initial velocity was 11km/s and its final velocity is 21km/s, the change in velocity is:
Δv = 21km/s - 11km/s = 10km/s
The time taken for the rocket to fire is given as 10 minutes, but let's convert it to seconds for consistency:
Δt = 10 minutes × 60 seconds/minute = 600 seconds
Now we can calculate the acceleration:
a = Δv / Δt = 10km/s / 600 seconds ≈ 0.017 km/s^2
To express the answer with two significant figures, we round it to:
a ≈ 0.017 km/s^2
Therefore, in the news conference, you would report that the acceleration imparted to the asteroid is approximately 0.017 km/s^2.