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 +4100 m/s, while rocket B has an initial velocity of +9400 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 -17 m/s2. What is the acceleration of rocket B?
just solve for a in
4100t - 17/2 t^2 = 9400t - a/2 t^2
a/2 t^2 = 5300t + 17/2 t^2
at^2 = 10600t + 17t^2
a = 10600/t + 17
To find the acceleration of rocket B, we can use the equation of motion:
s = ut + (1/2)at^2
Where:
s = displacement
u = initial velocity
a = acceleration
t = time
Given that the displacement of both rockets is zero, we have:
0 = (initial velocity of rocket B) * t + (1/2) * a * t^2
Since the initial velocity of rocket B is +9400 m/s, the equation becomes:
0 = 9400t + (1/2) * a * t^2
Since the displacement of rocket B is zero, the acceleration can be found by rearranging and solving for 'a':
a = -2 * (initial velocity of rocket B) / t
Substituting the given values:
a = -2 * 9400 / t
Thus, the acceleration of rocket B is -18800 / t m/s^2.