If both mass and velocity of a ball are tripled, the kinetic energy is increased by a factor of: 1) 3 . 2) 6 . 3) 9 . 4) 27 . 5) 81 .

When you triple both the mass (m) and the velocity (v) of a ball, the kinetic energy (KE) formula, KE = 0.5 * m * v², shows how the changes affect energy. Tripling the mass results in 3m, while tripling the velocity gives you (3v). The new kinetic energy becomes KE' = 0.5 * (3m) * (3v)² = 0.5 * (3m) * (9v²) = 13.5 * m * v², which is 27 times the original kinetic energy. So, the answer is 4) 27. Now imagine a soccer practice where players try to kick a ball with triple the force! Not only do they need to power up their muscles, but they'll also have to consider how much energy that ball will have on contact. With increased mass or speed, that ball will fly with an exciting force, making it even more crucial to strategize when aiming for the goal. Safety gear might need to be a priority too! To avoid common mistakes, remember that kinetic energy is not directly proportional to velocity but to the square of the velocity. A common pitfall is miscalculating by assuming doubling the velocity means doubling the kinetic energy. Instead, doubling the velocity actually increases the energy by four times, leading to unexpected outcomes. Always remember: speed bumps ahead on the math highway!