A high school senior vacationing in Jamaica for her senior class trip jumped off a 20 foot cliff into a pool of water. The height of the senior above the water is modeled by the function
h(t)=-t^2+t/4+5/4
where h(t) is the height of the senior above the water in feet t seconds after jumping off the cliff. How many seconds will it take for the senior to reach the water?
Where did you find this problem?
at t = 0, the senior has to be at 20 feet I think.
however your function shows her at 1.25 feet at t = 0
That is not right.
Moreover in real life h = Hi + Vi t -(1/2) g t^2
in the feet/seconds system
-(1/2) g t^2 is about -16 t^2
NOT -t^2
found it in my math homework... I thought it was a weird one too. Thank you
As it is stated it is impossible to solve because you can not start at both 20 and at 1.25 feet :)
To find the number of seconds it will take for the senior to reach the water, we need to determine the value of t when h(t) is equal to 0. This is because when the height above the water is 0, it means the senior has reached the water.
We can set up the equation:
h(t) = 0
Substituting the given function h(t) into the equation:
- t^2 + t/4 + 5/4 = 0
Now, we can solve this quadratic equation. To make it simpler, we multiply the entire equation by 4 to eliminate the fraction:
-4t^2 + t + 5 = 0
Next, we rearrange the equation in standard quadratic form, with the quadratic term first:
-4t^2 + t + 5 = 0
Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. In this case, the quadratic formula is the most straightforward method. The quadratic formula is:
t = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = -4, b = 1 and c = 5. Plugging these values into the quadratic formula:
t = (-1 ± √(1^2 - 4(-4)(5))) / (2(-4))
Simplifying further:
t = (-1 ± √(1 + 80)) / (-8)
t = (-1 ± √81) / (-8)
Now, we evaluate the square root:
t = (-1 ± 9) / (-8)
This gives two possible solutions for t:
1) t = (9 - 1) / (-8) = 8 / -8 = -1
2) t = (-9 - 1) / (-8) = -10 / -8 = 5/4
Since time cannot be negative, we discard -1 as a solution. Therefore, the only valid solution is t = 5/4.
It will take the senior 5/4 (or 1.25) seconds to reach the water.