A ball is thrown straight up into the air from the top of a building standing at 50 feet with an initial velocity of 65 feet per second the height of the ball in feet can be modeled by the following function: h(t)=-16t^2++16t+96 When does the ball reach its maximum height?

1 answer

Question:

A ball is thrown straight up into the air from the top of a building standing at 50 feet with an initial velocity of 65 feet per second the height of the ball in feet can be modeled by the following function: h(t)=-16t^2++16t+96 When does the ball reach its maximum height?

Answer:0.5 seconds (at 100 feet in the air). Step-by-step explanation:So, the height of the ball can be modeled by the function: [tex]h(t)=-16t^2+16t+96[/tex]Where h(t) represents the height in feet after t seconds. And we want to find its maximum height. Notice that our function is a quadratic. Therefore, the maximum height will occur at the vertex of our function. The vertex of a quadratic function in standard form is given by the formula: [tex](-\frac{b}{2a}, f(-\frac{b}{2a}))[/tex]In our function, a=-16; b=16; and c=96. Find the x-coordinate of the vertex: [tex]x=-\frac{(16)}{2(-16)}=1/2[/tex]So, the ball reaches its maximum height after 0.5 seconds of its projection. Notes: To find it’s maximum height, we can substitute 1/2 for our function and evaluate. So: [tex]h(1/2)=-16(1/2)^2+16(1/2)+96[/tex]Evaluate: [tex]h(1/2)=-4+8+96=100[/tex]So, the ball reaches its maximum height of 100 feet 0.5 seconds after its projection.

PLEASE READ!!!!!!!!!!!!!!!!!!!! Who is just tired of social media? I am. It's so offensive that the social media gets upset that kids dress in inappropriate clothes but on the street, you see 12-year-olds in the same (and worse clothes) is ok? When 12 year olds post themselves on the internet wearin...

the average annual cost of heating a home woth solar energy is $200 with an inital cost of $9000. During the month of may, the solar energy outlet is offering a 25% discount off the total cost. Express the discounted cost as a function of the number of years....

A plumber charges $50 per hour plus $75 service fee. Jackson hired a plumber to fix a leaky sink. What are the total charges of the plumber took 3 1/2 hours to complete the repairs...

Where did farming communities appear in about 5000 B.C.?
A. In both Egypt and Nubia
B. In the deserts of Upper Egypt
C. Between the Tigris and Euphrates rivers
D. In the delta of Upper Egypt...

What do legislators do when they take on 'casework'? *
A They analyze cases that are under appeal to the Supreme Court
B The appropriate the money that the government needs for federal project
C They authorize military action by issuing an official sta...

Does each situation describe a survey, an experiment, or an observational study?
Select Survey, Experiment, or Observational Study for each situation....