You throw a ball straight up from a rooftop 100 feet high with an initial speed of 112 feet per second. the function s (t )equals negative 16 t squared plus 112 t plus 100 models the ball's height above the ground, s (t )comma in feet, t seconds after it was thrown. during which time period will the ball's height exceed that of the rooftop?

the time period is 0 < t < 7 seconds  

Step-by-step explanation:

Data provided in the question:

Height of the rooftop = 100 feet

Initial speed = 112 feet per second

s(t ) = - 16t² + 112t + 100

here, s(t ) in feet

t in seconds

now,

for ball's to exceed rooftop

s(t ) = - 16t² + 112t + 100 > 100

or

⇒ - 16t² + 112t + 100 > 100

or

⇒ - 16t² + 112t > 100 - 100

or

⇒ - 16t² + 112t > 0

or

⇒ 16t² - 112t < 0

or

⇒ t( 16t - 112 ) < 0

thus,

t < 0 and    16t - 112 < 0

or

16t < 112

or

t < 7

Hence,

the time period is 0 < t < 7 seconds      [0 < t ; since time cannot be negative]

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