Rockets A and B are fired straight upward from rest. Rocket A is launched first and accelerates at 11.2 m/s2. Rocket B is launched 2.10 s after Rocket A and B accelerates at 14.6 m/s2. Solve for the moment in time when the rockets are separated by 484 m.

a) how long after rocket as launch are they separated by 482 m?

b) how high up is rocket a at this time?

c) how high up is rocket b at this time?

d) how fast is rocket a moving at this time?

e) how fast is rocket b moving at this time?

please help me!!

h1= heigth of first rocket

h2= height of second rocket

482=h1-h2=1/2 (11.2t^2-14.6(t-2.1)^2)
solve for t.

To solve this problem, we will use the equations of motion under constant acceleration. These equations are:

1) v = u + at
2) s = ut + (1/2)at²
3) v² = u² + 2as

Where:
- v is the final velocity
- u is the initial velocity
- a is the acceleration
- t is the time taken
- s is the displacement

a) To find the time when the rockets are separated by 482 m, we need to consider Rocket A since it is launched first. We'll use Equation 2:
482 = 0.5 * 11.2 * t²
Simplify the equation:
241 = 5.6t²
Rearrange the equation to isolate t:
t² = 241 / 5.6
t ≈ √43 = 6.56 seconds

Therefore, they are separated by 482 m approximately 6.56 seconds after Rocket A's launch.

b) To find the height of Rocket A at this time, we'll use Equation 2 again:
s = 0 * t + 0.5 * 11.2 * t²
s = 0.5 * 11.2 * (6.56)²
s ≈ 229.773 meters

Therefore, Rocket A is approximately 229.773 meters high at this time.

c) To find the height of Rocket B at this time, we'll consider the time difference between the launches of the two rockets. Rocket B is launched 2.10 seconds after Rocket A, so we subtract this time from the total time:
t' = 6.56 - 2.10
t' ≈ 4.46 seconds
Now, we can use Equation 2:
s = 0 * t' + 0.5 * 14.6 * t'²
s ≈ 0.5 * 14.6 * (4.46)²
s ≈ 144.623 meters

Therefore, Rocket B is approximately 144.623 meters high at this time.

d) To find the velocity of Rocket A at this time, we'll use Equation 1:
v = u + at
v = 0 + 11.2 * 6.56
v ≈ 73.472 m/s

Therefore, Rocket A is moving at approximately 73.472 m/s at this time.

e) To find the velocity of Rocket B at this time, we'll use Equation 1 again:
v = u + at
v = 0 + 14.6 * 4.46
v ≈ 65.116 m/s

Therefore, Rocket B is moving at approximately 65.116 m/s at this time.

I hope this helps! Let me know if you have any more questions.