how do you solve problems as such: if a person drops a water balloon off the rooftop of a 36 foot building, the height of the water balloon is give by the equation h=-16t^2+36, where t is in seconds. when will the water balloon hit the ground?

when it hits the ground, h = 0

-16t^2 + 36 = 0
t^2 = 36/16
t = 6/4 = 3/2 = 1.5

It will take 1.5 seconds

Just plug in the height of 36 ft into the equation given for the height, then you can solve for t by subtracting 36, then dividing by 16, and square rooting your answer (make sure to take the positive square root).

Well, let me tell you, this water balloon situation is really "going down" in the most literal sense! To find out when it will hit the ground, we can set the height equation h = -16t^2 + 36 equal to zero. Why zero? Because that's when the balloon reaches the ground, aka it's all "busted."

So, let's solve this equation!

-16t^2 + 36 = 0

Now, I'm no mathematician, but I've got a "gut feeling" about this one. To get rid of that -16, let's divide everything by -16. But remember, when you divide a negative number, it's like trying to share crayons with a grumpy clown – it flips the sign! So brace yourself, here we go!

t^2 - (36/-16) = 0

Simplifying that fraction, we get:

t^2 + (9/4) = 0

Now, let's isolate t by subtracting (9/4) from both sides:

t^2 = -9/4

Oh boy, negative numbers under the square root! Don't worry, we're not dealing with imaginary water balloons. What we have here is a "complex" situation. We can take the square root of both sides to rescue us from this puzzling predicament. So, let the square root party begin!

t = ±√(-9/4)

But remember kids, in the real world, square roots of negative numbers don't float! They sink, just like this water balloon. So, there's no real solution to this equation. In other words, this water balloon will never hit the ground! It's defying gravity, much like my attempts to juggle flaming bowling pins on a unicycle. What a showstopper, huh?

To find out when the water balloon hits the ground, we need to determine the value of t when the height, h, is equal to zero.

We can set h equal to zero in the equation h = -16t^2 + 36:

0 = -16t^2 + 36

Next, we can solve for t by rearranging the equation:

16t^2 = 36

Divide both sides of the equation by 16:

t^2 = 36/16

Simplify:

t^2 = 9/4

To solve for t, we take the square root of both sides:

t = ±√(9/4)

The square root of 9 is 3, and the square root of 4 is 2, so:

t = ±3/2

Since time cannot be negative in this scenario, we only consider the positive solution:

t = 3/2

Therefore, the water balloon will hit the ground after 3/2 seconds, or 1.5 seconds.

To figure out when the water balloon will hit the ground, we need to find the value of 't' when the height 'h' becomes zero. In other words, we need to solve the equation h = -16t^2 + 36 = 0.

Step 1: Set up the equation:
-16t^2 + 36 = 0

Step 2: Simplify the equation:
-16t^2 = -36

Step 3: Divide both sides of the equation by -16 to isolate 't^2':
t^2 = 36/16

Step 4: Take the square root of both sides to solve for 't':
t = ± √(36/16)

Step 5: Simplify the square root:
t = ± √(9/4)

Step 6: Simplify further:
t = ± (3/2)

Since we are looking for the time it takes for the water balloon to hit the ground, we can ignore the negative solution because time cannot be negative. Therefore, the water balloon will hit the ground at t = 3/2 seconds.

Note: The negative value indicates the time it would take for the water balloon to reach the maximum height before falling back down, but in this case, we are only concerned with when it hits the ground.