Question

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

Answer 1

Answer: 185,23 N

Explanation:

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

In the y-axis:

$Fy_{net}=Ft_{y}-Fp_{y}$

Where:

$Fy_{net}$ is the net vertical force acting on the astronaut

$Ft_{y}=Ft sin(20\°)$ is the vertical component of the thrust force (in the jetpack)

$Fp_{y}=Fp sin(45\°)$ is the vertical component of the planet gravitational force

$Ft=310 N$

$Fp=150 N$

In the x-axis:

$Fx_{net}=Ft_{x}-Fp_{x}$

Where:

$Fx_{net}$ is the net horizontall force acting on the astronaut

$Ft_{x}=Ft cos(20\°)$ is the horizontal component of the thrust force (in the jetpack)

$Fp_{x}=Fp cos(45\°)$ is the horizontal component of the planet gravitational force

Calculating the horizontal net force:

$Fx_{net}=Ft cos(20\°)-Fp cos(45\°)$

$Fx_{net}=310 N cos(20\°)-150 N cos(45\°)$

$Fx_{net}=185.23 N$ This is the net horizontal force acting on the astronaut.