Leap Off an Asteroid: Escape Earthly Gravity?

AI Thread Summary
To determine if a person can escape a 4.0-km-diameter asteroid with a mass of 1.0 x 10^14 kg by jumping, one must calculate the escape energy required for the asteroid and compare it to the energy generated from a jump. The escape energy per unit mass for the asteroid can be derived from its gravitational parameters. Additionally, the energy produced by a jump on Earth, which is approximately 50 cm, needs to be calculated to see if it meets or exceeds the escape energy. Using an energy approach is suggested as a more straightforward method for solving this problem. Ultimately, the feasibility of escaping the asteroid depends on these energy comparisons.
tjsingle
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Suppose that on Earth you can jump straight up a distance of 50 cm. Can you escape from a 4.0-km-diameter asteroid with a mass of 1.0 times 10^14 kg?
 
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You are going to need to write your attempt at a solution to get help I think.

If you are really stuck you can start with trying to see what force your legs produce when jumping on Earth.
 
I think it will be easier to use an energy approach.

What is the escape energy (per unit mass) for the asteroid? How much energy (per unit mass) you are able to generate in that jump?

AM
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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