Question

an astronaut in space
an astronaut and his space suit have a combined mass of 157 kg. the astronaut is using a 5.0 kg tool kit to repair a solar panel on the international space station. when the tether connecting the astronaut to the space station breaks, the astronaut (still holding the tool kit) starts to float away at 0.2 m/s.
21 calculate how far from the space station the astronaut will be after 1 minute. show your calculations and include units in your answer. (2 pts)
(a) (delta x=)
(b) calculate the momentum of the astronaut holding the tool kit as they both float away. show your calculations and include units in your answer. (4 pts)
(p = ) kg·m/s
the astronaut realizes that the only way to get back to the space station is to throw the tool kit.

Explanation:

Step1: Convert time to seconds

1 minute = 60 s

Step2: Use the speed - distance formula

The speed of the astronaut $v = 0.2\frac{m}{s}$, and the formula for distance $d=v\times t$. Substituting $v = 0.2\frac{m}{s}$ and $t = 60s$ into the formula, we get $d=0.2\frac{m}{s}\times60s$.
$d = 12m$

Step3: Calculate the total mass

The combined mass of the astronaut and the tool - kit $m=157kg + 5.0kg=162kg$

Step4: Calculate the momentum

The formula for momentum is $p = m\times v$. Substituting $m = 162kg$ and $v = 0.2\frac{m}{s}$ into the formula, we get $p=162kg\times0.2\frac{m}{s}=32.4kg\cdot m/s$

Answer:

(a) 12 m
(b) 32.4 kg·m/s