Dynamics. Acceleration of an resultant force

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

to the projection of the resultant force on the x-axis

Dynamics. Acceleration of an resultant force

Rocket mass m (kg)

Propulsion force F (N)

Angle to horizon α (degrees)

Free fall acceleration g (m/s²)

Calculate

Rocket acceleration a (m/s²)

 

Angle between acceleration and horizon β (degrees)

 

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