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Escape Speed

Calculate the escape speed of an object from a planet given gravitational constant, mass, and radius

Understand the Problem

Problem Statement

The program must accept three floating point values as G (gravitational constant), M (mass) and R (radius) of a planet. The program must calculate and print the escape speed of the object with precision up to 3 decimal places.

Formula: Escape speed = √(2GM/R)

Constraints

  • G, M, and R will be floating point values
  • All input values will be positive
  • Output must be formatted to exactly 3 decimal places
  • The gravitational constant G will be in appropriate units for the calculation

Examples

Example 1
Input
1.567 2.4783 3.4671
Output
1.497
Explanation

Using the formula √(2GM/R): √(2 × 1.567 × 2.4783 / 3.4671) = √(7.759 / 3.4671) = √(2.237) ≈ 1.497

Example 2
Input
1.9038 2.7920 4.3937
Output
1.555
Explanation

Using the formula √(2GM/R): √(2 × 1.9038 × 2.7920 / 4.3937) = √(10.619 / 4.3937) = √(2.417) ≈ 1.555

Solution

#include <stdio.h>
#include <math.h>

int main() {
    float g, m, r;
    scanf("%f %f %f", &g, &m, &r);
    
    float escape_speed = sqrt((2 * g * m) / r);
    printf("%.3f", escape_speed);
    
    return 0;
}
Time:O(1) - Constant time calculation
Space:O(1) - Uses only a constant amount of memory
Approach:

The C solution:

  1. Includes necessary headers: stdio.h for input/output and math.h for the sqrt() function
  2. Declares three float variables to store the input values
  3. Uses scanf() to read the three space-separated floating point numbers
  4. Calculates the escape speed using the formula sqrt((2 * g * m) / r)
  5. Prints the result formatted to 3 decimal places using printf("%.3f", escape_speed)

Visual Explanation

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