Brandon hit a baseball upward with an initial speed of 120 feet per second. How much later did Ollie catch the ball? Use the formula h = -16t squared + vt.
h = -1 6 t ^ 2 + vt
v = 120
h = - 16 t ^ 2 + 120 t
h = - 4 * 4 t ^ 2 + 4 * 30 t
h = 4 t ( - 4 t + 30 )
0 = 4 t ( - 4 t + 30 )
obviously solution :
t = 0
( initial point )
and
- 4 t + 30 = 0
- 4 t = - 30
- 4 t / 4 = - 30 / - 4
t = 30 / 4 = 2 * 15 / ( 2 * 2 ) = 15 / 2 = 7.5 s
hello :) i am an adv. algebra student and i often struggle w my homework, so i'd like to help those who are struggling with this problem. the formula for calculating maximum height is as follows: h=rt-16t^2. define your variables in a "let" statement and proceed by substituting as many variables as possible with information provided in the text. since we know the rate is 120 ft/s we can replace the "r." then you factor out the GCF to get "h=4t(30-4t)." if you distribute the "4t" you will get "h=120t-16t^2" which is the original equation. replace the "h" with a zero since solving for "h"--zero--is the goal. obviously "30-4t" has to equal zero so when you multiply that set of parenthesis by the outside "4t" you get zero. so since "30-4t" must equal zero, 30 and 4t must be equal to one another. so set up the equation: "30/4=4t/4" and solve for the variable "t." if you divided correctly, you should have written "t=7.5secs." hope i helped!!
Well, the equation you provided is for the height of an object thrown upward, but it doesn't tell us anything about Ollie catching the ball. Maybe Ollie didn't catch it at all, and it became a home run instead! Would you like me to calculate the height or time instead?
To find the time it took for Ollie to catch the ball, we need to set up an equation using the formula given: h = -16t^2 + vt.
In this case, we know that the initial velocity, v, is 120 ft/s, and assuming that Ollie catches the ball when it reaches the ground, the height, h, would be 0.
Therefore, we can set up the equation as follows: 0 = -16t^2 + 120t.
To solve this quadratic equation, we can set it equal to zero and apply the quadratic formula: t = (-b ± √(b^2 - 4ac)) / 2a.
For our equation, a = -16, b = 120, and c = 0. Plugging these values into the quadratic formula, we get:
t = (-120 ± √(120^2 - 4(-16)(0))) / 2(-16).
Simplifying further:
t = (-120 ± √(14400)) / -32.
t = (-120 ± 120) / -32.
This gives us two possible values for t: t = 0 or t = 7.5.
Since we are looking for the time later when Ollie catches the ball, we can disregard the t = 0 solution as it represents when the ball was hit initially. Therefore, Ollie catches the ball 7.5 seconds later.
So, to answer the question, Ollie catches the ball 7.5 seconds later.