Answer:
r2 = 1.25 × 10^(6) m
Explanation:
We are given;
Initial kinetic energy; K_1= 8.0 x 10^(7) J
Mass of planet zero; M = 4.0 x 10^(23) kg
Mass of space probe; m = 10 kg
Radius of planet zero; r1 = 2 × 10^(6) m
From conservation of energy, we can say that;
Initial potential energy + Initial kinetic energy = Final potential energy + Final kinetic energy
This is;
U1 + K1 = U2 + K2
Using formula for potential energy: U = GMm/r, we can write it as;
GMm/r1 + K1 = GMm/r2 + K2
Where Maximum distance = r2
At maximum distance from the center of Zero, K2 = 0.
Thus;
GMm/r1 + K1 = GMm/r2
Making r2 the subject, we have;
r2 = GMm/((GMm/r1)+ K1)
Where G is gravitational constant = 6.67 × 10^(-11) N/m²/kg2
Thus;
r2 = (6.67 × 10^(-11) × 4.0 x 10^(23) × 10)/((6.67 × 10^(-11) × 4.0 x 10^(23) × 10)/(2 × 10^(6)) + (8.0 × 10^(7)))
r2 = 1.25 × 10^(6) m
