Question

1. ignoring air resistance, an object in free fall will fall d feet in t seconds, where d and t are related by the algebraic model d = 16t². a.) how long will it take the object to fall 1412 ft? b.) if the object is in free fall for 14.5 sec after it is dropped, how high was the object when it was dropped? show your work.

Explanation:

Step1: Solve for t in part a

Given $d = 16t^{2}$, when $d = 1412$, we have $1412=16t^{2}$. First, divide both sides by 16: $\frac{1412}{16}=t^{2}$, so $t^{2}=88.25$. Then take the square - root of both sides. Since $t>0$ (time cannot be negative in this context), $t=\sqrt{88.25}\approx9.39$ seconds.

Step2: Solve for d in part b

Given $d = 16t^{2}$, when $t = 14.5$, substitute $t$ into the formula: $d=16\times(14.5)^{2}$. First, calculate $(14.5)^{2}=210.25$. Then multiply by 16: $d = 16\times210.25=3364$ feet.

Answer:

a. Approximately 9.39 seconds
b. 3364 feet