Question

for the following question, use the function h = - 16t² + v₀t + h₀, where h is the height of the object after time t, v₀ is the initial velocity, and h₀ is the initial height. an object is thrown upward from a height of 800 ft with an initial velocity of 80 ft/ s. how long will it take for the object to reach the ground?

Explanation:

Step1: Substitute values into formula

Given $h_0 = 800$, $v_0=80$, and $h = 0$ (ground - level), the formula $h=-16t^{2}+v_0t + h_0$ becomes $0=-16t^{2}+80t + 800$.

Step2: Simplify the equation

Divide the entire equation by -16: $t^{2}-5t - 50=0$.

Step3: Factor the quadratic equation

We get $(t - 10)(t + 5)=0$.

Step4: Solve for t

Set each factor equal to zero: $t-10 = 0$ gives $t = 10$; $t + 5=0$ gives $t=-5$. Since time cannot be negative in this context, we discard $t=-5$.

Answer:

$10$