The height of an object dropped from a 100-ft-tall building is given by h=-16t squared + 100. When will the object hit the ground? (Please provide steps/explanation to solve this problem.)
Oh, the object's falling, huh? Let's put on our mathematical goggles and figure out when it will hit the ground!
We have the equation h = -16t^2 + 100, where h represents the height and t represents time. We want to find out when the height is equal to zero, which means the object hits the ground. So let's set h = 0:
0 = -16t^2 + 100
To solve for t, we'll isolate the t^2 term by subtracting 100 from both sides:
-16t^2 = -100
Now, divide both sides by -16 to get t^2 alone:
t^2 = 100/16
Simplifying that, we have:
t^2 = 6.25
To solve for t, we take the square root of both sides:
t = ±√6.25
Now, be careful! The square root of 6.25 has two possible values: 2.5 and -2.5. But we're talking about time, and negative time doesn't make much sense in this context.
So we conclude that the object will hit the ground at t = 2.5 seconds. Keep an eye on that falling object and remember: gravity waits for no one, not even a clown!
To find when the object will hit the ground, we need to determine the value of time (t) when the height (h) is equal to zero.
The given equation for the height is h = -16t^2 + 100.
1. Set h = 0 in the equation to represent when the object hits the ground:
0 = -16t^2 + 100
2. Rearrange the equation:
-16t^2 + 100 = 0
3. Subtract 100 from both sides to isolate the quadratic term:
-16t^2 = -100
4. Divide both sides by -16 to create a simpler equation:
t^2 = 100/16
5. Simplify the right side of the equation:
t^2 = 25/4
6. Take the square root of both sides:
t = ±sqrt(25/4)
7. Simplify the right side:
t = ±(5/2)
Since negative time values are not meaningful in this context, we can exclude the negative solution. Thus, the object will hit the ground at t = 5/2 or 2.5 seconds.
Therefore, the object will hit the ground after 2.5 seconds.
Thanks for the help. :)
2/3
when it hits the ground is when h=0, so you just need to sub. h=0 into the given equation and solve for t
0= -16tsquare + 100
cheers