The escape velocity of a bullet from the surface of planet Y is 1695 m/s. Calculate the escape velocity from the surface of the planet X if the mass of planet X is 1.37 times that of Y, and its radius is 0.887 times the radius of Y (in m/s).
To calculate the escape velocity from the surface of planet X, we can use the following formula:
escape velocity (V) = √(2 * gravitational constant (G) * mass of the planet (M) / radius of the planet (R))
First, let's determine the gravitational constant for both planets using the escape velocity of planet Y. The escape velocity (V_y) of planet Y is given as 1695 m/s. With this information, we can rearrange the formula to solve for G:
G = V_y^2 * R_y / (2 * M_y)
Next, we'll determine the mass (M_x) and radius (R_x) of planet X using the given ratios. The mass of planet X (M_x) is 1.37 times that of planet Y:
M_x = 1.37 * M_y
And the radius of planet X (R_x) is 0.887 times the radius of planet Y:
R_x = 0.887 * R_y
Finally, we can substitute the values of G, M_x, and R_x into the escape velocity formula to calculate the escape velocity (V_x) of planet X:
V_x = √(2 * G * M_x / R_x)
Solving these equations step by step will allow us to calculate the escape velocity from the surface of planet X.