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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 +6500 m/s, while rocket B has an initial velocity of +8700 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 -13 m/s2. What is the acceleration of rocket B?

Respuesta :

Answer:

The acceleration of rocket B is -17.4 m/s².

Explanation:

Given that,

Initial velocity of rocket A = 6500 m/s

Final velocity of rocket B = 8700 m/s

Acceleration of rocket A = -13 m/s²

Displacement of both rocket is zero.

We need to calculate the time of rocket A

Using equation of motion

[tex]S_{A}=ut+\dfrac{1}{2}at^2[/tex]

Put the value into the formula

[tex]0=6500t+\dfrac{1}{2}\times(-13)\times t^2[/tex]

[tex]t=1000\ sec[/tex]

We need to calculate the acceleration of rocket B

Using equation of motion

[tex]S_{B}=ut+\dfrac{1}{2}at^2[/tex]

Put the value in the formula

[tex]0=8700\times1000+\dfrac{1}{2}\times a\times(1000)^2[/tex]

[tex]a=\dfrac{8700\times1000\times2}{(1000)^2}[/tex]

[tex]a=-17.4\ m/s^2[/tex]

Hence, The acceleration of rocket B is -17.4 m/s².

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