A tennis ball on Mars, where the acceleration due to gravity is $0.379 g$ and air resistance is negligible, is hit directly upward and returns to the same level $8.5$ s later. How high above its original point did the ball go?

검증된 단계별 안내

Identify the known values: The acceleration due to gravity on Mars is given as 0.379 times the acceleration due to gravity on Earth (g = 9.81 m/s²). Therefore, the acceleration due to gravity on Mars is 0.379 * 9.81 m/s².

Understand the motion: The ball is hit directly upward and returns to the same level after 8.5 seconds. This means the total time for the upward and downward journey is 8.5 seconds, so the time to reach the highest point is half of this, which is 4.25 seconds.

Use the kinematic equation for velocity: At the highest point, the velocity of the ball is 0 m/s. Use the equation v = u + at, where v is the final velocity (0 m/s), u is the initial velocity, a is the acceleration (-0.379 * 9.81 m/s², negative because it opposes the motion), and t is the time (4.25 s). Solve for the initial velocity u.

Use the kinematic equation for displacement: Once the initial velocity is found, use the equation s = ut + 0.5at² to find the maximum height s. Here, u is the initial velocity found in the previous step, a is the acceleration (-0.379 * 9.81 m/s²), and t is the time to reach the highest point (4.25 s).

Interpret the result: The value of s obtained from the previous step represents the maximum height above the original point that the ball reached.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Acceleration due to Gravity

Acceleration due to gravity is the rate at which an object accelerates when falling freely under the influence of gravity. On Mars, this acceleration is 0.379 times that on Earth, which affects the motion of objects. Understanding this concept is crucial for calculating the height reached by the tennis ball.

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. They are essential for solving problems involving projectile motion, like the tennis ball's trajectory. These equations allow us to relate time, initial velocity, final velocity, acceleration, and displacement to find the maximum height reached.

Projectile Motion

Projectile motion refers to the motion of an object thrown or projected into the air, subject only to acceleration due to gravity. In this scenario, the tennis ball's upward and downward journey is a classic example of projectile motion, where understanding the symmetry of the motion helps determine the peak height.