Use your graphing calculator to find how many seconds before the projectile hits the ground. Let y1 = −16t2 + 800t, or factor and solve for t algebraically
To find the time it takes for the projectile to hit the ground, we can use a graphing calculator to solve the equation −16t^2 + 800t = 0.
Here's how you can do it on a graphing calculator:
1. Turn on your graphing calculator and press the "Y=" button to enter the equation.
- Enter −16t^2 + 800t into the first function, represented as y1.
- This equation represents the height of the projectile with respect to time.
2. Press the "Graph" button to plot the function.
3. Look at the graph on the calculator screen. You should see a parabolic curve representing the projectile's height.
4. To find the x-intercepts of the graph (where the projectile hits the ground), use the "2nd" and "Calc" buttons (also known as "2nd" and "Trace") to access the calculator's "CALC" menu.
5. Select the "Zero" option from the CALC menu by pressing the respective number or button.
6. The calculator will prompt you to "Guess" a value close to where the projectile hits the ground. Use the arrow keys to move the guess closer, if needed.
7. Press the "Enter" or "Calculate" button to calculate the value of t when the projectile hits the ground.
The calculator will provide the value of t, which represents the number of seconds before the projectile hits the ground.
Alternatively, you mentioned factoring algebraically. Let's proceed with that method as well:
To factor and solve the equation algebraically, we have:
−16t^2 + 800t = 0
Step 1: Factor out common terms:
t(−16t + 800) = 0
Step 2: Set each factor equal to zero:
t = 0 (Due to the zero-product property)
−16t + 800 = 0
Step 3: Solve for t:
−16t = -800
t = -800/-16
t = 50
Therefore, the projectile will hit the ground after 50 seconds.