10. (4 pts) In physics, the escape velocity from a spherical planet (are there n

Question

10. (4 pts) In physics, the escape velocity from a spherical planet (are there non-s be computed using the formula pherical planets?...) can 2GM where G is the universal gravitational constant, M is the mass of the planet, and r is the distance from the planet's center of mass. Assume that you have double variables named G, M, and r with values already line of Java code that assigned. Write a singls computes the escape velocity based on those three variables and assigns it to a new double variable named v. Be sure to declare v. 11. (5 pts) Convert (11010)2 into base 10. Please show all your work! Minimal credit will be given for a solution that involves only counting. (5 pts) Check your result from the previous problem by converting it back into base 2. Again, please show all your work 12.

Explanation / Answer

Solution:

10.

public class EscapeVelocity {

   public static void main(String[] args) {
      
       //Declaring and Initializing the values of G,M,and R
       final double G = 6.673 * Math.pow(10, -11); //Universal Gravitational Constant (6.67 x 10-11 m3 kg-1 s-2)
       final double M = 5.98 * Math.pow(10, 24); //mass of the planet or moon (5.98 x 10^24 Kg)
       final double R = 6.38 * Math.pow(10, 6); // Radius of the planet i.e (6.38 x 10^6 m)
      
       //Using Escape Velocity formula i.e v = sqrt(2GM/R)
       double v = Math.sqrt(2*G*M/R);
      
       //Printing out the escape velocity.
       System.err.println("Escape velocity is "+v+"m/s");
   }
}

Sample Run:

Escape velocity is 11184.480402811645m/s

11.

( 11010 )2 = ( 26 )10

Explanation

Step 1:

Start at the rightmost digit. Take that digit and multiply with 20 (20 = 1). Multiple second digit with 21, third with 22...

In this example we have:

Step 2:

Add together all products

0 + 2 + 0 + 8 + 16 = 26

12.

Now lets do vice versa to prove

( 26 )10 = ( 11010 )2

Explanation

Step 1:

Write down the decimal number and continually divide by 2 to give a result and a remainder. The remainder is either a 1 or a 0.

In this example we have:

Step 2:

Read the remainders from bottom to top. i.e 11010

Note: I hope you understood the solution, If you need further details please do comment below, if you liked the solution then please do give a thumbs up.

0 * 20 = 0 * 1 = 0 1 * 21 = 1 * 2 = 2 0 * 22 = 0 * 4 = 0 1 * 23 = 1 * 8 = 8 1 * 24 = 1 * 16 = 16

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