Question

A large explosion causes wood and metal debris to rise vertically into the air with an initial velocity of 160 feet per second. The function h(t) = 160 t − 16 t 2 160t-16t2 gives the height of the falling debris above the ground, in feet, t t seconds after the explosion.

a. Use the given polynomial to find the height of the debris 2 second(s) after the explosion.
b. Factor the given polynomial completely.

Answer 1

a) The debris was 256 feet into the air after 2 seconds of the explosion.

b)

`h(t) = -16t(t-10)`

Explanation:

We are given the following in the question:

Initial Velocity = 160 feet per second

`h(t) = 160t-16t^2`

The above function gives the height in feet and t is seconds after the explosion.

a) Height of the debris 2 second(s) after the explosion.

We put t = 2 in the above function

`h(2) = 160(2)-16(2)^2 = 256`

Thus, the debris was 256 feet into the air after 2 seconds of the explosion.

b) Factor the polynomial

`h(t) = 160t-16t^2\\= 16t(10-t)\\=-16t(t-10)`