A solar sailplane is going from Earth to Mars. Its sail is oriented to give a solar radiation force of FRad = 8.60 × 102 N. The gravitational force due to the Sun is 173 N and the gravitational force due to Earth is 1.00 × 102 N. All forces are in the plane formed by Earth, Sun, and sailplane. The mass of the sailplane is 15,000 kg.

Respuesta :

Answer:

magnitude - 659.91 N

direction = 27.69 degree

Explanation:

The gravitational force due to sun is

Fs = 173 N

Fax = -173 N, Fay = 0 N

Gravitational force is

Fgx = 0 N

Fgy [tex]= -1.00\times 10^2 N = -100 N[/tex]

Assume Solar radiation force at an angle of 30 degree on sail plane is

[tex]F_R = 8.60\times 10^2 N[/tex]

[tex]F_{Rx} =860  cos 30 =744.78 N[/tex]

[tex]F_{Ry} = 8600 sin 30 = 430 N[/tex]

TOTAL FORCE  in x diretion= -173 + 0 + 744.48 = 571.48 N

and total force in y direction is

Fy = 0 - 100 + 430 = 330 N

Magnitude of force  [tex]= \sqrt{571.48^2 + 330^2} = 659.91 N[/tex]

[tex]Direction = tan^{-1}[ \frac{330}{571.48}] = 27.67 degree[/tex]