Pepe throws a penny off the empire state building. The penny's height above ground can be modelled using the equation h=-16.1t^2+5t+1250 where t is time in seconds. How high is Pepe when he throws the penny? How many seconds does it take the penny to hit the ground?
initial height is 1250 when t=0
it hits the ground when
-16.1t^2+5t+1250 = 0
To find how high Pepe is when he throws the penny, we need to determine the initial height, which is represented by the equation h = -16.1t^2 + 5t + 1250 when t = 0.
Let's substitute t = 0 into the equation:
h = -16.1(0)^2 + 5(0) + 1250
h = 0 + 0 + 1250
h = 1250
Therefore, Pepe is 1250 feet above the ground when he throws the penny.
To determine how many seconds it takes for the penny to hit the ground, we need to set the equation h = -16.1t^2 + 5t + 1250 equal to zero (since the ground is at h = 0).
-16.1t^2 + 5t + 1250 = 0
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:
t = (-b ± sqrt(b^2 - 4ac)) / (2a)
For this equation, a = -16.1, b = 5, and c = 1250.
t = (-(5) ± sqrt((5)^2 - 4(-16.1)(1250))) / (2(-16.1))
Simplifying further:
t = (-5 ± sqrt(25 + 80560)) / (-32.2)
t = (-5 ± sqrt(80585)) / (-32.2)
Since we're looking for the time it takes for the penny to hit the ground, we're only interested in the positive value for t.
Plugging this into a calculator, we find:
t ≈ 7.6 seconds
Therefore, it takes approximately 7.6 seconds for the penny to hit the ground.