Question

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 +4600 m/s, while rocket B has an initial velocity of +8200 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 -18 m/s2. What is the acceleration of rocket B?

Answer 1

`a_2\ =\ -33.65\ m/s^2`

Step-by-step explanation:

Given,

For the first rocket,

• Initial velocity of the first rocket A =
  `u_1\ =\ 4600\ m/s.`

• Acceleration of the first rocket =
  `a_1\ =\ -18\ m/s^2`

For the second rocket,

• Initial velocity of the second rocket B =
  `u_2\ =\ 8200 m/s.`
• Displacement of both the rockets A and B = s = 0 m

Fro the first rocket,

Let 't' be the time taken by the first rocket A for whole the displacement

`\therefore s\ =\ u_1t\ +\ (1)/(2)a_1t^2\\\Rightarrow 0\ =\ 4600t\ -\ 0.5* 18t^2\\\Rightarrow t\ =\ (4600)/(0.5* 18)\\\Rightarrow t\ =\ 511.11 sec`

Let
`a_2` be the acceleration of the second rocket B for the same time interval

from the kinematics,

`\therefore s\ =\ ut\ +\ (1)/(2)at^2\\\Rightarrow s\ =\ u_2t\ +\ (1)/(2)a_2t^2\\\Rightarrow a_2\ =\ (2s\ -\ 2u_2t)/(t^2)\\\Rightarrow a_2\ =\ (0\ -\ 2u_2t)/(t^2)\\`

`\Rightarrow a_2\ =\ -(2u_2)/(t)\\\Rightarrow a_2\ =\ -(2* 8600)/(511.11)\\\Rightarrow a_2\ =\ -33.65\ m/s^2`

Hence the acceleration of the second rocket B is -33.65\ m/s^2.