Algebra problem

Question

A large explosion causes metal debris to fly into the air with an initial velocity of 112 feet per second. The polynomial

112t -16t squared

gives the height of the debris, in feet, ttseconds after the explosion. A) Use the given polynomial to find the height of the debris 2 second(s) after the explosion. 

Answer: After 2 second(s), the height is____  feet. ?

B) Factor the given polynomial completely. 

Answer: 16t(7−t) 

  

(Make sure you use the correct variable). C) How long after the explosion does the debris hit the ground? 

Answer 1

h(t) = -16t^2 + 112t

h(2) =- 16(2)^2 + 112(2) = -64 + 224 = 160 feet high after 2 seconds

it hits the ground when h(t) = 0

-16^2 +112t = 0

-16t(t-7) = 0 set the factor t-7 equal to zero t-7=0, t=7 seconds set t=0 that's when it started at ground level

t = 7 seconds when it hits the ground

-16t^2 +112t factors by dividing by -16t to get -16t(t-7)

or divide by 16t to get 16t(7-t)