Question

(a) What is the escape speed on a spherical asteroid whose radius is 500 km and whose gravitational acceleration at the surface is 3.0 mlsz? (b) How far from the surface will a particle go if it leaves the asteroid's surface with a radral speed of 1000 m/s? (c) With what speed will an object hit the asteroid if it is dropped from 1000 km above the surface?

Answer 1

Answer:

(a) 1732.05 m/sec

(b) h = 166.66 km

(c) 2449.48 m/sec  

Step-by-step explanation:

We have given radius of the asteroid R = 500 KM

Acceleration due to gravity at the asteroid $g=3m/sec^2$

(a) We have to find the escape velocity

We know that escape velocity is given by

$v_e=\sqrt{2Rg}=\sqrt{2\times 500\times 10^3\times 3}=1732.05m/sec$

(b) We have given initial velocity u = 1000 m/sec

At maximum height velocity will be zero

So final velocity v = 0 m/sec

From third equation of motion

$v^2=u^2+2gh$

$0^2=1000^2-2\times 3\times h$

h = 166.66 km

(c) h = 1000 km

We have to find the final velocity

From third equation of motion

$v^2=u^2+2gh$

$V^2=0^2+2\times 3\times 1000000$

v = 2449.48 m/sec