Mathematics, 24.03.2020 21:43, macho123

A projectile is launched from ground level with an initial velocity of v0 feet per second. It's height in feet t seconds after launch is given by s= -16t^2+v0t. Find the time the projectile will reach a height of 192ft when v0= 112 ft per second

Answers: 1

Show answers

Answers

answered: granthazenp5e9mj

Step-by-step explanation:

The pull of gravity in feet per second squared is 32. Going backwards from that (which requires integration in calculus) gives us eventually the position function which has a leading coefficient of -16t-squared. The v0 is our initial vertical velocity. The position equation for this situation then is

s(t)=-16t^2+112t

We are asked to find at what times (yes, there are 2 of them!) when the position of the projectile will be at 192 feet. Because of the nature of a parabola, the object will pass a certain number of feet going up, but then because of gravity, will pass by that same number of feet coming back down. Our position of 192 feet is subbed in for s(t) to give us

192=-16t^2+112t and we are asked to solve for t. The only way we can do that is to put everything on one side of the equals sign and set the quadratic equal to 0 and factor. At the same time I am going to factor out a -16 to make the numbers a bit more manageable when we use the quadratic formula.

-16(t^2-7t+12)=0

By the Zero Product Property, either -16 = 0 which of course it doesn't!, or

t^2-7t+12=0

Factor that using the quadratic formula or whatever method you've been taught that is the best for you and get the times that the object is 192 feet in the air is at 3 seconds and again at 4 seconds.

Along the lines of parabolic motion, if the object passes 192 at 3 and then again at 4 seconds, that means that somewhere in between 3 and 4 seconds it reached its max height. To be exact, at 3.5 seconds. To find the max height of the object, sub 3.5 in for t in the original position equation to get the height at 3.5 seconds:

s(3.5)=-16(3.5)^2+112(3.5) to get that the max height of the projectile is 196 feet. That's just a bit extra. I am a teacher after all of both calculus and physics and can't let a teaching moment go by!! ;)

answered: Guest

i think is 3 and 6. this took me 10 min to think.hope to and hope that my answer is brainliest.(follow me )

answered: Guest

38 dollars is your answer.

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 13:30, kah36

In the field of thermodynamics, rankine is the unit used to measure temperature. one can convert temperature from celsius into rankine using the formula c= r/1.8 - 273, what is the temperature in celcius corresponding to r degrees rankine.

Answers: 2

continue

Mathematics, 21.06.2019 17:30, aprilreneeclaroxob0c

Mrs. morton has a special reward system for her class. when all her students behave well, she rewards them by putting 3 marbles into a marble jar. when the jar has 100 or more marbles, the students have a party. right now, the the jar has 24 marbles. how could mrs. morton reward the class in order for the students to have a party?

Answers: 3

continue

Mathematics, 21.06.2019 20:00, stonerbabyy

Someone answer asap for ! the boiling point of water at an elevation of 0 feet is 212 degrees fahrenheit (°f). for every 1,000 feet of increase in elevation, the boiling point of water decreases by about 2°f. which of the following represents this relationship if b is the boiling point of water at an elevation of e thousand feet? a. e = 2b - 212 b. b = 2e - 212 c. e = -2b + 212 d. b = -2e + 212

Answers: 1

continue

Mathematics, 21.06.2019 23:30, tumadreeve7852

Select the correct answer and solve for y

Answers: 2

continue

Do you know the correct answer?

A projectile is launched from ground level with an initial velocity of v0 feet per second. It's heig...