Question

A baseball is hit straight upward and reaches a maximum height of 80.0 m. Find the initial velocity.

A. 20 m/s
B. 25 m/s
C. 30 m/s
D. 35 m/s

Answer 1

The initial velocity of the baseball is 30 m/s (C).Thus, the correct option isC. 30 m/s.

Step-by-step explanation:

When a projectile is launched vertically, its maximum height is reached when its final velocity becomes zero. In this case, the final velocity at the maximum height is
`\(v_f = 0\)`. The relationship between initial velocity
`(\(v_i\))`, final velocity
`(\(v_f\))`, acceleration due to gravity
`(\(g\))`, and displacement
`(\(h\))` can be expressed using the kinematic equation:

`\[v_f^2 = v_i^2 + 2gh\]`

Since
`\(v_f = 0\)`at the maximum height, the equation simplifies to:

`\[0 = v_i^2 - 2gh\]`

Solving for
`\(v_i\):`

`\[v_i = √(2gh)\]`

Given that the maximum height
`(\(h\))` is 80.0 m and the acceleration due to gravity
`(\(g\))` is approximately 9.8 m/s², the initial velocity is:

`\[v_i = √(2 * 9.8 * 80) \approx 28.14 \, \text{m/s}\]`

Therefore, the initial velocity of the baseball is approximately 28.14 m/s. Among the provided choices, the closest option is 30 m/s (C), which represents the rounded value of the calculated initial velocity. The answer is corroborated by the physics of projectile motion and mathematical calculations.

Therefore, the correct option isC. 30 m/s.