The height of a ball thrown from the top of a building can be modeled by the equation, where h is the height in feet and t is time in seconds.
h(t)=−16t^2+55t+214
I already got the height of the building correct....=214 feet
I got the maximumheight of ball =1.7188 secs
i got height of the ball= 261.2656 feet.
BUT I need help with D)
(d) The time it takes for the ball to reach the ground:
thank you kindly
just solve h(t) = 0
t = 5.76
To find the time it takes for the ball to reach the ground, we need to determine when the height of the ball becomes zero, since this indicates that the ball has reached the ground.
Given the equation for the height of the ball: h(t) = -16t^2 + 55t + 214, we can set h(t) equal to zero and solve for t:
0 = -16t^2 + 55t + 214
To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula, which states that for an equation in the form of ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = -16, b = 55, and c = 214. Plugging these values into the quadratic formula, we can calculate the solutions for t:
t = (-55 ± √(55^2 - 4(-16)(214))) / (2(-16))
Simplifying this equation will give us the values of t when the ball reaches the ground.