To determine the maximum height reached by a ball thrown straight up, we can use the kinematic equation for vertical motion:
Δy = (v₀² - v²) / (2g)
where: Δy is the displacement or height traveled v₀ is the initial velocity v is the final velocity (which is 0 at the maximum height) g is the acceleration due to gravity (approximately 9.8 m/s²)
Let's plug in the values:
v₀ = 36.12 m/s v = 0 m/s g = 9.8 m/s²
Δy = (36.12² - 0²) / (2 * 9.8)
Calculating this expression:
Δy = (1305.4944) / (19.6)
Δy ≈ 66.6 meters
Therefore, the ball will reach a maximum height of approximately 66.6 meters.