If I threw a ball vertically at an initial speed of 34.5 m/s, how many seconds would it take to reach its maximum height?

3.8

To determine how long it takes for the ball to reach its maximum height, you need to consider the concept of projectile motion. When an object is thrown vertically upward, its initial velocity will gradually decrease until it reaches its maximum height. At the maximum height, the object's velocity is momentarily zero before it starts to fall back down due to gravitational acceleration.

In this scenario, the problem can be solved using the following formula:

Time = (Final Velocity - Initial Velocity) / Acceleration

Since the ball is thrown vertically upward and its initial velocity is 34.5 m/s, the final velocity at the highest point will be zero. The acceleration used in this formula will be the acceleration due to gravity, which is approximately 9.8 m/s².

Plugging in the values:

Time = (0 - 34.5) m/s / (-9.8 m/s²)

Simplifying the expression:

Time = -34.5 m/s / -9.8 m/s²

The negative signs cancel out, resulting in:

Time = 34.5 / 9.8 seconds

Calculating this expression:

Time ≈ 3.52 seconds

Therefore, it will take approximately 3.52 seconds for the ball to reach its maximum height.