Answer:
2.87 km/s
Explanation:
radius of planet, R = 1.74 x 10^6 m
Mass of planet, M = 7.35 x 10^22 kg
height, h = 2.55 x 10^6 m
G = 6.67 x 106-11 Nm^2/kg^2
Use teh formula for acceleration due to gravity
![g=\frac{GM}{R^{2}}](https://tex.z-dn.net/?f=g%3D%5Cfrac%7BGM%7D%7BR%5E%7B2%7D%7D)
![g=\frac{6.67\times 10^{-11}\times 7.35\times 10^{22}}{1.74^{2}\times 10^{12}}](https://tex.z-dn.net/?f=g%3D%5Cfrac%7B6.67%5Ctimes%2010%5E%7B-11%7D%5Ctimes%207.35%5Ctimes%2010%5E%7B22%7D%7D%7B1.74%5E%7B2%7D%5Ctimes%2010%5E%7B12%7D%7D)
g = 1.62 m/s^2
initial velocity, u = ?, h = 2.55 x 10^6 m , final velocity, v = 0
Use third equation of motion
![v^{2}=u^{2}-2gh](https://tex.z-dn.net/?f=v%5E%7B2%7D%3Du%5E%7B2%7D-2gh)
0 = v² - 2 x 1.62 x 2.55 x 10^6
v² = 8262000
v = 2874.37 m/s
v = 2.87 km/s
Thus, the initial speed should be 2.87 km/s.