Question on Physics problem of time and distance

[Daniol10]

I have this problem I am doing for college algebra. Its been giving me a lot of trouble and i have know idea how to handle it. the problem is that is a ball that were thrown from the top of a 96 foot building traveling at an initial velocity of 80 ft/s would travel from there all the way to the ground how many seconds would it reach the ground(a) and the top of the building(b)? they also give an equation for that represents the distance traveled (d=96+80t-16t^2) I've been stuck on the problem for a good while and have now idea how to go by it

 

[tiny-tim]

Welcome to PF!

Hi Daniol10! Welcome to PF!

(try using the X₂ button just above the Reply box )

ok, so you have an equation d = 96 + 80t - 16t²,

and you need to sove it for (a) d = 0, and (b) d = 96.

sooo … just put that value of d into the equation, and solve it as an ordinary quadratic equation in t …

what do you get? ​

 

[Daniol10]

Thanks! I had forgotten about the quadratic formula. I ended up with 6 sec for (a) and 5 sec for (b)

 

[tiny-tim]

Fine!

btw, you'll notice that both equations have another solution …

eg for (a) it's -1 s, which is when it would have had to be thrown from the ground to follow the same trajectory! ​

 

[asteriatic]

Hi there,

It seems like you are dealing with a problem involving time and distance in the context of a ball being thrown from a building. To solve this problem, we can use the equation d = 96 + 80t - 16t^2, where d represents the distance traveled, t represents time, and 96 is the initial height of the building.

To find the time it takes for the ball to reach the ground (a), we can set d = 0, since the ball will be at the ground when it reaches a distance of 0. This gives us the equation 0 = 96 + 80t - 16t^2. We can then solve for t by using the quadratic formula or by factoring the equation. Once we have t, we will have the time it takes for the ball to reach the ground.

To find the time it takes for the ball to reach the top of the building (b), we can set d = 96, since the ball will be at the top of the building when it reaches a distance of 96 feet. This gives us the equation 96 = 96 + 80t - 16t^2. Again, we can solve for t using the quadratic formula or by factoring the equation.

I would recommend reviewing the concepts of solving quadratic equations and using equations to solve problems involving time and distance. It may also be helpful to draw a diagram or make a table to organize the information given in the problem.

Best of luck with your problem and your studies in college algebra!