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Chapter 1: Q57P (page 428)

You are exploring a distant planet. When your spaceship is in a circular orbit at a distance of 630 km above the planet鈥檚 surface, the ship鈥檚 orbital speed is 4900 m/s. By observing the planet, you determine its radius to be 4.48 x 106 m. You then land on the surface and, at a place where the groundis level, launch a small projectile with initial speed 12.6 m/s at an angle of 30.8颅 above the horizontal. If resistance due to the planet鈥檚 atmosphere is negligible, what is the horizontal range of the projectile?

Short Answer

Expert verified

The horizontal range of the projectile is 26.63 m.

Step by step solution

01

Identification of the given data

Distance above the planet surface =630km=630000

Orbital speed =4900m/s

Radius of the planet 4.48x106m

Initial speed = 12.6 m/s

Angle = 30.8 颅

02

Calculation of the mass of the planet

g=GMR2g=V2脳(R+h)R2g=49002脳4.48脳106+630004.468脳1062g=6.11m/s2

Horizontal range

d=v02g脳sin2蠒d=13.626.11脳sin(2脳30.8)d=26.63m

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