Question

How long will it take a 200 kg stationary man in space to travel 20 m if he throws a 10 kg object at a velocity of 30 m/s?

Answer 1

To solve this problem, we can use the principle of conservation of momentum. The total momentum before the man throws the object is zero, as both the man and the object are stationary. After the man throws the object, the total momentum of the system (man + object) will be conserved.

Let's denote the velocity of the man after throwing the object as v, and the velocity of the object after being thrown as V. According to the principle of conservation of momentum:

Initial momentum of the system = Final momentum of the system

(0) = (mass of the man) * (final velocity of the man) + (mass of the object) * (final velocity of the object)

(0) = (200 kg) * v + (10 kg) * V

Now we can substitute the given values and solve for v:

(200 kg) * v + (10 kg) * 30 m/s = 0 (since the object is thrown with a velocity of 30 m/s)

v = - (10 kg) * 30 m/s / (200 kg)

v = - 1.5 m/s

So the man's velocity after throwing the object is -1.5 m/s. Since the man is in space with no external forces acting on him, his velocity will remain constant at -1.5 m/s. Now we can calculate the time it takes for the man to travel 20 m with a velocity of -1.5 m/s:

time = distance / velocity

time = 20 m / (-1.5 m/s)

time = -13.33 seconds

Since time cannot be negative in this context, we can ignore the negative sign and the answer is approximately 13.33 seconds.


I think this is correct double check this pls

Answer 2

Step-by-step explanation:

If my memory serves me well, this is recoil. It has the formula

`[(m_m*v_m)+(m_o*v_o)]_b=[(m_m*v_m)+(m_*v_o)]_a`

This says that the mass of the man times his velocity plus the mass of the object times its velocity BEFORE he threw the object has to be equal to the same information AFTER he threw the object, since momentum has to be conserved. Just like energy, it cannot be created nor destroyed. Filling in, we can find the velocity of the man AFTER he threw the object:

`[(200*0)+(10*0)]_b=[(200*v)+(10*30)]`

Simplifying, that gives us

0 = 200v + 300 and

-300 = 200v so

-1.5 m/s = v

It's negative because he recoils in the opposite direction of the direction of the object. That's what recoil is. That's his velocity, so now we can sub that into d = rt to find out how long it takes him to travel 20 m:

(the 20 will be negative here because he is moving in a direction opposite of the object's)

-20 = -1.5t so

t = 13 and 1/3 seconds