Final answer:
To find the escape velocity from Planet X, the relationship between mass and radius of the planets to their escape velocities is used. For Planet X, the mass is 1.35 times and radius is 0.855 times that of Planet Y. The calculation results in an escape velocity of 2089 m/s for Planet X.
Step-by-step explanation:
To calculate the escape velocity from the surface of Planet X given the escape velocity from Planet Y and the differing mass and radius of Planet X, we use the formula for escape velocity v = √(2Gm/r), where G is the gravitational constant, m is the mass of the planet, and r is the radius of the planet. The escape velocity is proportional to the square root of the mass and inversely proportional to the square root of the radius.
Given that the mass of Planet X is 1.35 times that of Planet Y and the radius of Planet X is 0.855 times that of Planet Y, we can use the ratio VeX = VeY √(mX/mY) / √(rX/rY), where VeX is the escape velocity from Planet X, VeY is the escape velocity from Planet Y, mX/mY is the mass ratio and rX/rY is the radius ratio.
Therefore, VeX = 1727 m/s √(1.35)/√(0.855). Calculating this yields an answer of 2089 m/s, which corresponds to option C.