An astronaut floating in space is trying to use her jetpack to get back to her
space station, but she is being pulled away by a nearby planet, as shown in
the image below. Her jetpack provides a constant thrust of 310 N. If she
angles her jetpack in such a way that it cancels out the vertical force due to
the planet's gravity, what is her net horizontal force?
Jetpack
Thrust
310 N
; 200
450
Planet's
gravitational pull
150 N

185,23 N

Explanation:

If we draw a free bodey diagram of the astronaut, we will have the following:

In the y-axis:

Where:

is the net vertical force acting on the astronaut

is the vertical component of the thrust force (in the jetpack)

is the vertical component of the planet gravitational force

In the x-axis:

Where:

is the net horizontall force acting on the astronaut

is the horizontal component of the thrust force (in the jetpack)

is the horizontal component of the planet gravitational force

Calculating the horizontal net force:

This is the net horizontal force acting on the astronaut.

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y