calc 1 help

[colby_smith]

1. The traffic department of a town wishes to put a warning sign reading "Slow Down, Stoplight Ahead" sufficiently in advance of the stoplight for oncoming motorists to have time to slow down and stop at the light. If automobiles can decelrate at the rate of 5 ft/sec^2 and if the maximum speed allowed on the road is 30 mi/hr, hor far in advance of the light should the warning sign be placed to permit motorists to stop in time?

2. Suppose that fluid flows out of the bottom of a cone-shaped vessel at the rate of 3 cu ft/min. If the height of the cone is three times the radius, how fast is the height of the fluid decreasing when the fluid is 6 inches deep in the middle?

3. A conical tank is 14 ft. across the top and 12 ft. deep. Water is flowing in at the rate of 30 cu ft/min. and flowing out at a rate of 20 cu ft/min. How fast is the slope of the graphchanging when x=32?

Thanks for your help

 

[Deleted member 4993]

1. The traffic department of a town wishes to put a warning sign reading "Slow Down, Stoplight Ahead" sufficiently in advance of the stoplight for oncoming motorists to have time to slow down and stop at the light. If automobiles can decelrate at the rate of 5 ft/sec^2 and if the maximum speed allowed on the road is 30 mi/hr, hor far in advance of the light should the warning sign be placed to permit motorists to stop in time?

2. Suppose that fluid flows out of the bottom of a cone-shaped vessel at the rate of 3 cu ft/min. If the height of the cone is three times the radius, how fast is the height of the fluid decreasing when the fluid is 6 inches deep in the middle?

3. A conical tank is 14 ft. across the top and 12 ft. deep. Water is flowing in at the rate of 30 cu ft/min. and flowing out at a rate of 20 cu ft/min. How fast is the slope of the graphchanging when x=32?

Thanks for your help

These are excellent problems from:
[h=1]Calculus: an intuitive and physical approach[/h]Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[colby_smith]

These are excellent problems from:
Calculus: an intuitive and physical approach

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.

alright, let me get my notes, give me a second

 

[colby_smith]

on the first one, v=a(t) so i'm thinking i'd want to start with 8=30(t) or something like that, i'm trying to use a similar approach I had on a previous problem were you had to calculate how long a train was in motion traveling 400 yards. on the other two, I have absolutly no idea where to even begin.

 

[colby_smith]

one other thing, the function f(x)=1/(1-x^2), would the domain be (-Infinity, -1)U(-1,1)U(1, Infinity)

 

[Deleted member 4993]

1. The traffic department of a town wishes to put a warning sign reading "Slow Down, Stoplight Ahead" sufficiently in advance of the stoplight for oncoming motorists to have time to slow down and stop at the light. If automobiles can decelrate at the rate of 5 ft/sec^2 and if the maximum speed allowed on the road is 30 mi/hr, hor far in advance of the light should the warning sign be placed to permit motorists to stop in time?

Use the equation:

v² = u² + 2* a * s

you have:

u = initial velocity = 30 mph = 44 ft/sec

v = final velocity = 0

a = - 5 ft/sec²

s = distance travelled

Now finish it.....

2. Suppose that fluid flows out of the bottom of a cone-shaped vessel at the rate of 3 cu ft/min. If the height of the cone is three times the radius, how fast is the height of the fluid decreasing when the fluid is 6 inches deep in the middle?

3. A conical tank is 14 ft. across the top and 12 ft. deep. Water is flowing in at the rate of 30 cu ft/min. and flowing out at a rate of 20 cu ft/min. How fast is the slope of the graphchanging when x=32?

Thanks for your help

.

 

[Deleted member 4993]

1. The traffic department of a town wishes to put a warning sign reading "Slow Down, Stoplight Ahead" sufficiently in advance of the stoplight for oncoming motorists to have time to slow down and stop at the light. If automobiles can decelrate at the rate of 5 ft/sec^2 and if the maximum speed allowed on the road is 30 mi/hr, hor far in advance of the light should the warning sign be placed to permit motorists to stop in time?

2. Suppose that fluid flows out of the bottom of a cone-shaped vessel at the rate of 3 cu ft/min. If the height of the cone is three times the radius, how fast is the height of the fluid decreasing when the fluid is 6 inches deep in the middle?

Start with drawing an inverted cone.

We have solved problem like that in this forum - search for it.

for example:

http://www.freemathhelp.com/forum/threads/68543

There are more - you just have to search for it.

3. A conical tank is 14 ft. across the top and 12 ft. deep. Water is flowing in at the rate of 30 cu ft/min. and flowing out at a rate of 20 cu ft/min. How fast is the slope of the graph changing when x=32?

Thanks for your help

does not make sense - fix your post.

 

[colby_smith]

v² = u² + 2* a * s

can you tell me how you came up with this function? also, would it matter that v=44 ft/sec instead of 44 ft/sec^2

 

[Deleted member 4993]

v² = u² + 2* a * s

can you tell me how you came up with this function? also, would it matter that v=44 ft/sec instead of 44 ft/sec^2

That is known as Galileo's 3rd equation. Others are:

v = u + a*t

s = s₀ + u*t + 1/2*a*t²

In the earlier post above - I had a mistake. It should have been:

u = initial velocity = 30 mph = 44 ft/sec

v = final velocity = 0

 

[colby_smith]

That is known as Galileo's 3rd equation. Others are:

v = u + a*t

s = s₀ + u*t + 1/2*a*t²

In the earlier post above - I had a mistake. It should have been:

u = initial velocity = 30 mph = 44 ft/sec

v = final velocity = 0

thanks for the help, as for the third question, i'm not sure what he meant by the wording of that question, i'll have to go to the math lab on campus to figure it out.