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An astronaut is standing on the surface of a planetary satellite that has a radius of 1.74 × 10^6 m and a mass of 7.35 × 10^22 kg. An experiment is planned where a projectile needs to be launched straight up from the surface.
What must be the minimum initial speed of the projectile so it will reach a height of 2.55 × 10^6 m above this satellite's surface? (G = 6.67 × 10^-11 N · m^2/kg^2)

Respuesta :

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

[tex]g=\frac{GM}{R^{2}}[/tex]

[tex]g=\frac{6.67\times 10^{-11}\times 7.35\times 10^{22}}{1.74^{2}\times 10^{12}}[/tex]

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

[tex]v^{2}=u^{2}-2gh[/tex]

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.