Suppose that an object is dropped from the top of the leaning tower of pisa, 185 feet above the ground. The objects height in feet, h, after t seconds is given by the following ntion: h(t)= -16t^2+185. How long will it take for the object to hit the ground?
when it hist the ground the height is zero, right?
so just solve
-16t^2+185 = 0
To find out how long it will take for the object to hit the ground, we need to find the value of "t" when the height "h(t)" becomes zero. In other words, we need to solve the equation h(t) = 0.
The given equation for the object's height is h(t) = -16t^2 + 185.
Substituting h(t) with 0, we get:
0 = -16t^2 + 185.
To solve this quadratic equation, we'll set it equal to zero and use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the value of x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = -16, b = 0, and c = 185. Substituting these values into the quadratic formula, we have:
t = (-0 ± √(0 - 4(-16)(185))) / (2(-16))
Simplifying further:
t = ± √(0 + 11840) / (-32)
t = ± √(11840) / (-32)
t = ± √(4 * 2960) / (-32)
t = ± (2√2960) / (-32)
t = ± (√2960) / (-16)
Since time cannot be negative, we discard the negative solution:
t = √2960 / (-16)
Calculating the value, we get:
t ≈ -3.55
However, in this context, we disregard negative time because it doesn't make sense. Therefore, the object will hit the ground after approximately 3.55 seconds.