Question

A rocket with a mass of 4.50×10⁵kg is in flight. Its thrust is directed at an angle of 55.0∘ above the horizontal and has a magnitude of 7.50×10⁶. Find the magnitude of the rocket's acceleration. Express your answer correct to two decimal places.

Answer 1

The magnitude of the rocket's acceleration is approximately 15.61 m/s².

To find the magnitude of the rocket's acceleration, we break down the thrust force into horizontal (F horizontal) and vertical (F vertical​ ) components. The horizontal acceleration (a horizontal​ ) is determined by dividing F horizontal by the mass (m). In the vertical direction, the acceleration (a vertical) involves dividing F vertical by m. Considering gravitational acceleration (g≈9.8m/s^2), the total vertical acceleration (a total vertical) is the sum of a vertical​ and −g.

The magnitude of the rocket's acceleration (a rocket​ ) is then calculated using the Pythagorean theorem:
`a_rocket=√(a^2 horizontal+a^2 total vertical)`. Substituting the provided values yields an acceleration of approximately 15.61 m/s².