Question

For the following question, use the function h = - 16t² + vot + h(0), where h is the height of the object after time t, vo is the initial velocity, and h(0) is the initial height. An object is thrown upward from a height of 880 ft with an initial velocity of 96 ft/ s. How long will it take for the object to reach the ground?​

Answer 1

`Answer:\ \boxed {11}\ s`

Explanation:

`h=-16t^2+v_0t+h_0\\\\h_0=880 \ ft\ \ \ \ \ \ v_0=96\ ft/s\\\\`

When reaching the ground, height h=0

Hence,

`0=-16t^2+96t+880`

Divide both parts of the equation by -16:

`t^2-6t-55=0\\\\t^2+(-11t+5t)-55=0\\\\(t^2-11t)+(5t-55)=0\\\\t(t-11)+5(t-11)=0\\\\(t-11)(t+5)=0\\\\t-11=0\\\\t=11\ s\\\\t+5=0\\\\t=-5\\otin(t > 0)`