Question

an object is thrown downward with an initial velocity of 7 feet per second. the relationship between the distance s it travels and time t is given by s = 7t + 16t². how long does it take the object to fall 78 feet? it takes seconds for the object to fall 78 feet. question help: video ebook

Explanation:

Step1: Set up the equation

We are given $s = 7t+16t^{2}$ and $s = 78$. So, $16t^{2}+7t - 78=0$.

Step2: Use the quadratic formula

For a quadratic equation $ax^{2}+bx + c = 0$ ($a = 16$, $b = 7$, $c=-78$), the quadratic formula is $t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. First, calculate the discriminant $\Delta=b^{2}-4ac=(7)^{2}-4\times16\times(-78)=49 + 4992=5041$.

Step3: Find the values of t

$t=\frac{-7\pm\sqrt{5041}}{2\times16}=\frac{-7\pm71}{32}$. We have two solutions: $t_1=\frac{-7 + 71}{32}=\frac{64}{32}=2$ and $t_2=\frac{-7 - 71}{32}=\frac{-78}{32}$ (rejected since time cannot be negative).

Answer:

2