Question

a large explosion causes wood and metal debris to rise vertically into the air with an initial velocity of 112 feet per second. the polynomial 112t - 16t^2 gives the height of the falling debris above the ground, in feet, t seconds 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: (make sure you use the correct variable). note: if you plug t = 2 into your factored expression in part b, you should get the same answer as you did in part a. check it. why is this true? does this mean your factorization is correct? think about it, but no response is required.

Explanation:

Step1: Find height at t = 2

Substitute t = 2 into the polynomial $h(t)=112t - 16t^{2}$.
$h(2)=112\times2-16\times2^{2}$

Step2: Calculate the result

First, calculate $16\times2^{2}=16\times4 = 64$ and $112\times2 = 224$. Then $h(2)=224 - 64=160$.

Step3: Factor the polynomial

Factor out the greatest - common factor from $112t - 16t^{2}$. The GCF of 112 and 16 is 16, and both terms have a factor of t. So $112t - 16t^{2}=16t(7 - t)$.

Answer:

A) 160
B) $16t(7 - t)$