# Dynamics. Acceleration of an resultant force

This online calculator illustrates the solution of the example problem on dynamics.

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Created: 2024-01-06 06:05:10, Last updated: 2024-01-30 22:41:15

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Problem:
When a rocket of mass m is launched, the thrust force of its engine, equal to F, is directed at an angle α to the horizon. Taking free fall acceleration g equal to 10 m/s², find the acceleration of the rocket a, i.e. the modulus of the acceleration and the angle between the acceleration and the horizon β.

Solution:

After inspecting the figure, it is clear that the resultant force R can be found through the cosine theorem, the modulus of acceleration is equal toR/m, and the angle can be found through the tangent, i.e., the ratio of the projection of the resultant force on the y-axis
$R_y=Fsin\alpha-mg$
to the projection of the resultant force on the x-axis
$R_x=Fcos\alpha$

#### Dynamics. Acceleration of an resultant force

Rocket acceleration a (m/s²)

Angle between acceleration and horizon β (degrees)

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PLANETCALC, Dynamics. Acceleration of an resultant force