If an object is dropped from a height of 200 feet, the function h(t) = -16 t^2 + 200 gives the height of the object after t seconds. Approximately, when will the object hit the ground?
0 = 200 -16 t^2
16 t^2 = 200
t = sqrt (25/2) =3.544 seconds
Well, let me put on my mathematical clown shoes and juggle some numbers for you! We have the function h(t) = -16 t^2 + 200, and we want to find when the height is 0 (because that's when it hits the ground!). So, we set h(t) = 0:
-16 t^2 + 200 = 0
Now let's solve for t. We can divide both sides by -16:
t^2 - 12.5 = 0
Next, we can subtract 12.5 from both sides:
t^2 = 12.5
Taking the square root of both sides, we get:
t ≈ ±3.54
Now, we only care about the positive value because time can't be negative in this context. So, approximately, the object will hit the ground after about 3.54 seconds. But remember, this is just an approximation - the real timing may have a few circus tricks up its sleeve!
To find when the object hits the ground, we need to find the time when the height is zero.
Let's set h(t) = 0 and solve for t:
-16t^2 + 200 = 0
Divide both sides by -16:
t^2 - 12.5 = 0
Now, we solve for t by taking the square root of both sides:
t = ±√(12.5)
Since time cannot be negative in this context, we can ignore the negative solution:
t = √(12.5)
Now, we can approximate the value of √(12.5):
√(12.5) ≈ 3.54 (rounded to two decimal places)
Therefore, the object will hit the ground approximately 3.54 seconds after being dropped.
To find the time when the object hits the ground, we need to determine when its height, h(t), equals zero. In this case, h(t) represents the height of the object at time t.
Given the function h(t) = -16t^2 + 200, we can set h(t) = 0 and solve for t.
0 = -16t^2 + 200
Rearranging the equation:
16t^2 = 200
Divide both sides by 16:
t^2 = 12.5
Taking the square root of both sides:
t = ±√12.5
Since time cannot be negative in this context, we only consider the positive solution:
t ≈ √12.5
Using a calculator, we find that √12.5 is approximately 3.54.
Therefore, the object will hit the ground approximately 3.54 seconds after it is dropped.
h(t) = -16 t^2 + 200
Ground = 0 feet
0 = -16 t^2 + 200
Solve for t.