I have no idea how to even start this, can someone kinda "point me in the right direction" so to speak.
-Compute the time(t) it will take for a tool to fall to the ground when a worker drops from the top of the building.
-Function:h(t)=-16t^2th0 where t is the time in seconds, h is the height in feet at time t, and h0 is the height of the building
-so if the bulding is 500 feet high, then h0 = 500 and the function would be h(t)=-16t^2 + 500
-when the tool reaches the ground, the height of the tool is zero(0) so the function would be: -16t^2 + 500 = 0
-Solve this quadratic equation for t
-16t^2 + 500 = 0
16t^2 = 500
t^2 = 500/16 = 31.25
t = √31.25 = appr 5.59 seconds
If I was graphing this it'll open upwards right?
h(t) = 500 - 16 t^2
opens down (sheds water)
if the ground were not at h=0 the tool would keep falling into negative h. (down a deep hole)
The tool is at its maximum height, h = 500 at the beginning when h = 500 and t = 0
It is also below 500 feet in the imaginary time before t = 0, as if it were thrown up and reached 500 feet at zero speed just as you hit your stopwatch:)
Oh ok, thank you so much!
Question
What does Psychrometer mean?
Answer Choices
* A tool used to measure air temperature
* A tool used to measure the speed of wind
* A tool used to measure the relative humidity in the atmosphere
To compute the time it will take for the tool to fall to the ground, you will need to solve the quadratic equation -16t^2 + 500 = 0.
To solve this equation for t, you can follow these steps:
Step 1: Start with the quadratic equation: -16t^2 + 500 = 0.
Step 2: Move the constant term (500) to the right side of the equation, changing the sign: -16t^2 = -500.
Step 3: Divide both sides of the equation by the coefficient of t^2 (-16) to isolate the term t^2: t^2 = 500/16.
Step 4: Simplify the right side of the equation: t^2 = 31.25.
Step 5: Take the square root of both sides to solve for t: t = ±√31.25.
Therefore, the time it will take for the tool to fall to the ground is t = ±√31.25.
Note that since time cannot be negative in this context, we discard the negative solution. Thus, the time it will take for the tool to fall to the ground is t = √31.25.