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

Step-by-step 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.