dolution

When an object moves

under the influence of constant force (without air resistance),

its path is parabolic. This is the path of a ball

thrown near the surface of a planet or other celestial

object. Suppose two balls are simultaneously thrown

upward at a 45_ angle on two different planets. If their

initial velocities are both 30 mph, then their rectangular

coordinates (in feet) can be determined by the function

Æ’1×2 = x –

g

1922

x2 ,

where g is the acceleration due to gravity. The value

of g will vary with the mass and size of the planet.

(Source: Zeilik, M., S. Gregory, and E. Smith, Introductory

Astronomy and Astrophysics, Saunders College

Publishers.)

On Earth, g = 32.2, and on Mars, g = 12.6. Find

the two equations, and determine the difference in the

horizontal distances traveled by the two balls.