the function pt 16t2120t37 approximates the height in feet o

the function p(t) =-16t^2+120t+37 approximates the height in feet of a rock launched by physics students with a catapult from a roof. t is the time of the flight in seconds.

1- how tall is the building?

2-how long does it take to reach the top of it\'s flight? her w high does it get?

how long does it take to hit the ground?

Solution

how tall is the building?

at t=0 sec, the rock is on the top of the building

so, p(0)= is the height of the building

p(0)=-16*0+120*0+37=37

height of the building = 37 feet.

2)

to find maximum height,

f\'(x)=0

-32t+120=0

t=120/32

t=3.75

therefore,

it takes 3.75 sec to reach the top of its flight

and maximum height = p(3.75) = -16*(3.75)²+120*3.75+37

= -16*(14.0625)+450+37

= -225 +450+37

= 225+37

= 262 feet.

how long does it take to reach the ground , means height =0 that gives p(t)=0

0=-16t²+120t+37

solving this quadratic equation, we get

t = 7.8,-0.3 sec

t cant be negative

therefore,

t= 7.8 sec

therefore,

it takes 7.8 sec to hit the ground