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Work through a classic 2-D kinematics and projectile motion problem from OpenStax University Physics Volume 1, Chapter 4, Problem 49, involving an astronaut kicking a soccer ball on Mars. Learn to break down the initial velocity of 16.0 m/s at 34° above horizontal into x- and y-components, apply constant-acceleration kinematics in the vertical direction to determine time of flight, and use horizontal motion principles to calculate the range. Discover how to perform sanity checks on algebra and arithmetic using computer algebra systems and online calculators to verify problem setup and catch common sign or unit errors. Compare the projectile motion results between Mars and the Moon to build intuition about how gravitational acceleration affects range, with Mars yielding approximately 64.2 m range and the Moon producing roughly 145.3 m range for the same initial conditions.
