If a stone is tossed from the top of a 250 meter building, the height of the stone as a function of time is given by h(t) = -9.8t2 – 10t + 250, where t is in seconds, and height is in meters. After how many seconds will the stone hit the ground? Round to the nearest hundredth’s place; include units in your answer.
When the stone hits the , the heiht will be zero:
-9.8t^2 - 10t + 250 = 0,
Solve using the Quadratic Formula and
get:
t = -5.59 and 4.57s.
Use positve value:
t = 4.57s.
To find the time it takes for the stone to hit the ground, we need to find the value of t when the height, h(t), is equal to zero. This is because when the stone hits the ground, its height is zero.
So we can set the equation h(t) = 0 and solve for t.
Let's start with the given equation: h(t) = -9.8t^2 - 10t + 250
Setting h(t) to zero, we have:
0 = -9.8t^2 - 10t + 250
To solve this quadratic equation, we can use the quadratic formula. The quadratic formula is given by:
t = (-b ± √(b^2 - 4ac)) / (2a)
In our equation:
a = -9.8, b = -10, and c = 250.
Let's substitute these values into the quadratic formula:
t = (-(-10) ± √((-10)^2 - 4(-9.8)(250))) / (2(-9.8))
Simplifying further:
t = (10 ± √(100 + 9800)) / (-19.6)
t = (10 ± √(9900)) / (-19.6)
Now we can calculate the values inside the square root:
√(9900) ≈ 99.50
Substituting this value back into the equation:
t = (10 ± 99.50) / (-19.6)
Now we can calculate the two possible solutions:
t1 = (10 + 99.50) / (-19.6) ≈ -5.10
t2 = (10 - 99.50) / (-19.6) ≈ 5.10
Since time cannot be negative in this context, we can ignore the negative solution.
Therefore, the stone will hit the ground after approximately 5.10 seconds (rounded to the nearest hundredth).
So, the stone will hit the ground after 5.10 seconds.