Answer :
Answer:
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]