Answer to Question #120973 in Physics for jonell

Question

The asteroid 101955 Bennu is currently being explored by NASAs OSIRIS-REX mission. bunnu has a mass of 6.24*10^10 kg and a radius of 282 m. A probe on the surface of bennu moves by making small hops of the surface. if the probe hops directly upwards with an initial velocity of 0.0453 m/s, it will reach a maximum height of ..... m before coming back down

Answer 1

To solve this problem, compute the acceleration due to gravity for this asteroid from the equilibrium between the force of gravity and the universal force of gravity:

$$mg=G\frac{Mm}{R^2},\\\space\\ g=\frac{GM}{R^2}.$$

The height that the hopper will reach can be found from energy conservation principle: the hopper's kinetic energy (assuming no losses) fully turns into potential energy:

$$\frac{mv^2}{2}=mgh,\\ h=\frac{v^2}{2g}=\frac{(vR)^2}{2GM},\\\space\\h=\frac{(0.0453\cdot282)^2}{2\cdot6.673\cdot10^{-11}\cdot6.24\cdot10^{10}}=19.6\text{ m}.$$