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 +6700 m/s, while rocket B has an initial velocity of +9700 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 -12 m/s2. What is the acceleration of rocket B?
6700t - 6t^2 = 0
t = 1116.66
9700(1116.66) + a/2 (1116.66^2) = 0
a = -17.37 m/s^2
To find the acceleration of rocket B, we can use the equation of motion:
displacement (d) = initial velocity (u) * time (t) + (1/2) * acceleration (a) * time^2
Since both rockets start side by side and end up side by side with zero displacement, their displacements are equal to zero.
For rocket A:
d = 0,
u = +6700 m/s,
a = -12 m/s^2.
Plugging the values in the equation of motion:
0 = (6700 m/s) * t + (1/2) * (-12 m/s^2) * t^2
Simplifying the equation:
0 = 6700t - 6t^2
Now let's solve for 't' using the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Here, a = -6, b = 6700, and c = 0.
t = (-6700 ± √(6700^2 - 4(-6)(0))) / (2(-6))
Calculating further:
t = (-6700 ± √(44890000)) / (-12)
t = (-6700 ± 6700) / (-12)
We have two possible values for 't':
t1 = 0 (ignoring this solution since rocket A already has a non-zero velocity),
t2 = -13400 / (-12) = 1116.67 seconds (approximately)
Now, to find the acceleration of rocket B, we will use the formula:
acceleration (a) = (final velocity - initial velocity) / time
Since both rockets are side by side after time 't', the final velocity of rocket B is also zero. Thus:
a = (0 - 9700 m/s) / 1116.67 s
Calculating the acceleration:
a ≈ -8.69 m/s^2.
Therefore, the acceleration of rocket B is approximately -8.69 m/s^2.