A cannonball is fired across a field. Its height above the ground after t seconds is given by -16t^2+104. How long does it take for the ball to reach its maximum height of 169 feet?
169 = -16t^2 + 104
16t^2 = -65
no solution,
it will never reach 169 ft, the maximum height is 104 ft when t = appr 2.5 seconds
If -16t^2+104 mean :
- 16 t ^ 2 + 104 t
then :
in google type :
quadratic equation online
Wfen you see list of results click on :
Free Online Quadratic Equation Solver: Solve by Quadratic Formula
Select one of method.
Then in rectangle type :
- 16 t ^ 2 + 104 t = 169
and click option : solve it !
You will see solutions step - by - step
In this case solution are :
t = 13 / 4 sec = 3.25 sec
To find the time it takes for the cannonball to reach its maximum height of 169 feet, we need to set the height equation equal to 169 and solve for t.
Given height equation: -16t^2 + 104 = 169
Subtracting 104 from both sides: -16t^2 = 169 - 104 = 65
Dividing both sides by -16: t^2 = 65 / -16
Taking the square root of both sides: t = √(65 / -16)
However, since time cannot be negative in this context, we can ignore the negative square root and focus on the positive square root.
So, t = √(65 / -16)
Using a calculator, we find that t ≈ 1.62 seconds.
Therefore, it takes approximately 1.62 seconds for the cannonball to reach its maximum height of 169 feet.
To find the time it takes for the cannonball to reach its maximum height of 169 feet, we need to set the height equation equal to 169 and solve for time (t).
The height equation is given as:
h(t) = -16t^2 + 104
Setting h(t) = 169, we have:
169 = -16t^2 + 104
Rearranging the equation by subtracting 104 from both sides:
-16t^2 = 169 - 104
Simplifying:
-16t^2 = 65
Next, divide both sides by -16 to isolate t^2:
t^2 = 65 / -16
t^2 = -4.0625
Since we cannot have a negative value for time, we know there is no real solution for this equation. This indicates that the cannonball will not reach a maximum height of 169 feet.
Please note that there may be an error in the given information or the equation provided. Double-check the values and equations to ensure accuracy.