Answer:
[tex]\beta=63.85^{\circ}[/tex] from the vertical OR [tex]16.15^{\circ}[/tex] from horizontal.
Explanation:
Given:
Thrust of launching the rocket, [tex]F=5\times 10^6\ N[/tex]
angle of launch from the horizontal, [tex]\theta=37^{\circ}[/tex]
mass of the rocket, [tex]m=200000\ kg[/tex]
Now the direction of acceleration due to the thrust force is in the direction of force:
[tex]a=\frac{F}{m}[/tex]
[tex]a=\frac{5000000}{200000}[/tex]
[tex]a=25\ m.s^{-2}[/tex]
And the acceleration due to gravity is always directed towards the center of the earth i.e. vertically downwards.
Since acceleration is a vector quantity we, approach accordingly:
[tex]\tan\beta=\frac{a\cos\theta}{g}[/tex]
[tex]\tan\beta=\frac{25\cos37^{\circ}}{9.8}[/tex]
[tex]\beta=63.85^{\circ}[/tex] from the vertical OR [tex]16.15^{\circ}[/tex] from horizontal.
