Two rockets are flying in the same direction and are side by side at the instant their retrorockets fire. Rocket A has an initial velocity of + 6400 m/s, while rocket B has an initial velocity of + 9800 m/s. After a time t both rockets are again side by side, the displacement of each being zero. The acceleration of rocket A is - 15 m/s2. What is the acceleration of rocket B?
To find the acceleration of rocket B, we need to use the concept of relative motion and the equations of motion.
Let's consider the motion of rocket A as the reference frame. In this frame, the initial velocity of rocket A is +6400 m/s, and its acceleration is -15 m/s^2. We also know that after time t, both rockets are again side by side, with zero displacement.
Since both rockets are traveling in the same direction, the relative velocity between the two rockets will be the difference of their individual velocities. In this case, the relative velocity between rocket A and rocket B is:
Relative velocity = Velocity of Rocket B - Velocity of Rocket A
Plugging in the given values, we have:
Relative velocity = (+9800 m/s) - (+6400 m/s)
= +3400 m/s
Now, using the equation of motion:
Displacement = Initial velocity * time + (1/2) * acceleration * time^2
For rocket B, the displacement is zero since it ends up side by side with rocket A. So, we can write:
0 = (+9800 m/s) * t + (1/2) * acceleration * t^2
Simplifying this equation, we get:
0 = 9800t + (1/2) * acceleration * t^2
Since we are looking for the acceleration of rocket B, let's solve for acceleration:
(1/2) * acceleration * t^2 = -9800t
Multiplying both sides by 2, we have:
acceleration * t^2 = -19600t
Dividing both sides by t to isolate acceleration, we get:
acceleration = -19600t / t^2
acceleration = -19600 / t
Therefore, the acceleration of rocket B is -19600 / t m/s^2, where t is the time elapsed.