Question

What is its maximum height? Its initial vertical speed is 8.5 m/s and the acceleration of gravity is 9.8 m/s2. Neglect air resistance. Answer in units of m.

Answer 1

The maximum height reached by an object thrown upwards with an initial vertical speed of 8.5 m/s, under gravity (9.8 m/s²), is 3.685 meters.

Step-by-step explanation:

To determine the maximum height reached by an object with an initial vertical speed and subject to gravity, we utilize the kinematic equations for uniformly accelerated motion. Using the equation V₁² = V₀² - 2g(y - y₀), where V₁ is the final velocity (0 m/s at maximum height), V₀ is the initial vertical speed (8.5 m/s), g is the acceleration due to gravity (9.8 m/s²), and y - y₀ is the change in height, we can solve for the maximum height reached. The formula rearranges to y - y₀ = V₀² / (2g). Plugging in the values, we get:

y - y₀ = (8.5 m/s)² / (2 × 9.8 m/s²)

y - y₀ = 72.25 m²/s² / 19.6 m/s²

y - y₀ = 3.685 m

Thus, the maximum height the object will reach above its initial position is 3.685 meters.