Problem: A ball is dropped from the top of a building that is 250 feet tall. The height h of the ball in feet after t seconds is modeled by the function h = -16t2 +250. How long will it take for the ball to reach the ground? Round your answer to the nearest tenth if necessary.
0 = -16t^2 + 250
16t^2 = 250
t^2 = 250/16
t = √250/4 = appr 3.95
or 4.0 sec to the nearest tenth
Well, let's see. If the ball hits the ground, it means that its height is zero. So we can set the function equal to zero, like this: -16t^2 + 250 = 0.
Now, let's solve for t. We can start by subtracting 250 from both sides of the equation, which gives us -16t^2 = -250.
Next, we can divide both sides of the equation by -16, resulting in t^2 = 15.625.
Finally, we can take the square root of both sides to solve for t. But be careful, because the square root of 15.625 is a little tricky to calculate.
So, after much thought and calculation, my answer is... drumroll please... approximately 3.95 seconds!
Please note that this answer is rounded to the nearest tenth, as requested.
To find the time it takes for the ball to reach the ground, we need to find when the height of the ball, h, equals 0.
Therefore, we need to solve the equation -16t^2 + 250 = 0.
Let's solve for t:
-16t^2 + 250 = 0
First, let's subtract 250 from both sides:
-16t^2 = -250
Next, let's divide both sides by -16 to isolate t^2:
t^2 = 250/16
t^2 = 15.625
Now, let's take the square root of both sides to solve for t:
t = √(15.625)
t ≈ 3.95
Therefore, the ball will take approximately 3.95 seconds to reach the ground.
To find the time it takes for the ball to reach the ground, we need to find the value of t when the height, h, is equal to 0.
Given that the height of the ball is modeled by the function h = -16t^2 + 250, we can set h to 0 and solve for t:
0 = -16t^2 + 250
To solve this equation, we need to isolate the variable t. We can start by subtracting 250 from both sides of the equation:
-250 = -16t^2
Next, we divide both sides of the equation by -16 to isolate t^2:
t^2 = -250 / -16
Simplifying further:
t^2 = 15.625
To solve for t, we take the square root of both sides of the equation:
t = √15.625
Calculating the square root:
t = 3.95
Therefore, it will take approximately 3.95 seconds for the ball to reach the ground.