Question

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.

Answer 1

magnitude - 659.91 N

direction = 27.69 degree

Step-by-step explanation:

The gravitational force due to sun is

Fs = 173 N

Fax = -173 N, Fay = 0 N

Gravitational force is

Fgx = 0 N

Fgy
`= -1.00* 10^2 N = -100 N`

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

`F_R = 8.60* 10^2 N`

`F_(Rx) =860  cos 30 =744.78 N`

`F_(Ry) = 8600 sin 30 = 430 N`

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
`= √(571.48^2 + 330^2) = 659.91 N`

`Direction = tan^(-1)[ (330)/(571.48)] = 27.67 degree`