Question

question 25 of 29
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 165 n. if she angles her jetpack in such a way that it cancels out the vertical force due to the planets gravity, what is her net horizontal force?
jetpack thrust 165 n
45°
20°
planets gravitational pull 80 n
a. 98.5 n toward the space station
b. 132.6 n toward the space station
c. 53.3 n away from the space station
d. 112.8 n away from the space station

Explanation:

Step1: Resolve jet - pack thrust into horizontal component

The jet - pack thrust is $F = 165$ N and the angle with the horizontal is $\theta=20^{\circ}$. The horizontal component of the jet - pack thrust is given by $F_x=F\cos\theta$. So, $F_x = 165\times\cos(20^{\circ})$. Using a calculator, $\cos(20^{\circ})\approx0.9397$, then $F_x=165\times0.9397 = 155.0505$ N.

Step2: Resolve gravitational pull into horizontal component

The gravitational pull is $F_g = 80$ N and the angle with the horizontal is $45^{\circ}$. The horizontal component of the gravitational pull is $F_{gx}=F_g\cos(45^{\circ})$. Since $\cos(45^{\circ})=\frac{\sqrt{2}}{2}\approx0.7071$, then $F_{gx}=80\times0.7071 = 56.568$ N.

Step3: Calculate net horizontal force

The net horizontal force $F_{net,x}=F_x - F_{gx}$. Substitute the values: $F_{net,x}=155.0505-56.568 = 98.4825\approx98.5$ N. The positive sign indicates the direction is toward the space station.

Answer:

A. 98.5 N toward the space station