A tennis ball is thrown upward from the top of a 680 foot high building at a speed of 56 feet per second. The tennis ball's height above ground can be modeled by the equation. When does the tennis ball hit the ground?

t = 8.5 s

Explanation:

Kinematic equation of the movement of the tennis ball that is thrown upwards:

y = y₀ + v₀*t - ½ g*t² Equation (1)

Where:

y : position of the ball as a function of time

y₀ : Initial position of the ball

t: time

g: acceleration due to gravity in m/s²

Known data

g = 32 ft/s²

y₀ = 680 ft

v₀ = 56 ft/s

Calculation of the time it takes for the ball to thit the ground

We replace data en the equation (1)

y = y₀ + v₀*t - ½ g*t²

0 = 680 + (56) * t - ½ (32) * t²

16*t² - (56) * t - 680 = 0 equation (2)

solving equation (2) quadratic:

t₁ = 8.5 s

t₁ = - 5 s

Time cannot be negative so the time it takes for the ball to hit the ground is t = 8.5 s