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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?

Respuesta :

valeriagonzalez0213

Answer:

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

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