Question

Two meteoroids are heading for earth. Their speeds as they cross the moon's orbit are 2.0 km/s .

A) The first meteoroid is heading straight for earth. What is its speed of impact?

B) The second misses the earth by 4500 km . What is its speed at its closest point?

Answer 1

(a) we know that,

                       

    it becomes

                     

       here,

                  m = mass of asteroid,

                  v2 = final velocity or impact velocity

                 v1 = initial velocity = 2 km/s

                 G = gravitational constant = 6.67 × 10^-11 m³ kg^-1 s^-2 = 6.67*10^{-20} km³ kg^-1 s-2

                 M = Mass of Earth = 6*10^{24} kg

                 R = radius of Earth = 6.371*10^{3}km

                 d = distance of moon = 384*10^{3} km

therefore,

             

             

          

         

Speed of impact for first meteoroid is 10.9346 km/s

(b)    for second meteoroid is

                         

          here,

                  v2 = final velocity

                 v1 = initial velocity = 2 km/s

                 G = gravitational constant = 6.67 × 10^-11 m³ kg^-1 s^-2 = 6.67*10^{-20} km³ kg^-1 s-2

                 M = Mass of Earth = 6*10^{24} kg

                 R = radius of Earth = 6.371*10^{3}km

                 d = distance of moon = 384*10^{3} km

in formula, 4500 (in km) is the distance

then,