Two rockets are flying in the same direction and are side by side at the instant their retrorockets fire. rocket a has an initial velicity of +5800m/s, while rocket b has an initial velocity of +8600m/s. after a time t both rockets are again side by side, the displacement of each being zero. the acceleration of rocket a is -15m/s^2. what is the acceleration of rocket b?

The acceleration of rocket B is -22.24 m/s²

Explanation:

Two rockets are flying in the same direction and are side by side at the

instant their retrorockets fire

That means they started from the same point at the same time

Rocket A has an initial velocity of  5800 m/s

Rocket B has an initial velocity of 8600 m/s

After a time t both rockets are again side by side, the displacement of

each being zero

That means they are in the same position again → s = 0

The acceleration of rocket A is  -15 m/s²

We need to find the acceleration for rocket B

We can find the time from the information of rocket A by using the

rule → s = u t + a t²

where s is the displacement, u is the initial velocity, a is the

acceleration, and t is the time

→ s = 0 , u = 5800 m/s , a = -15 m/s²

Substitute these values in the rule

→ 0 = 5800 t + (-15) t²

→ 0 = 5800 t - 7.5 t²

Add 7.5 t² for both sides

→ 7.5 t² = 5800 t

Divide both sides by 7.5 t

→ t = 773.3 s

The time for the both rocket to have displacement zero is 773.3 s

Now we can find the acceleration of the rocket B by using the same

rule above

→ u = 8600 m/s , t = 773.3 , s = 0

→ 0 = (8600)(773.3) + a (773.3)²

→ 0 = 6650380 + 298996.445 a

Subtract 6650380 from both sides

→ -6650380 = 298996.445 a

Divide both sides by 298996.445

→ a = -22.24 m/s²

The acceleration of rocket B is -22.24 m/s²

no. dot product   =0 when vecs at right angles