Hello everyone, alright, I did as many problems as I was able to before coming to the forums. I don't want people to think I'm abusing the services here, my calculus professor give us 5 different assignments each weekend so these few problems are actually relatively small compared to what was assigned. XD
Problem #1
An object is launched straight upward from a platform above ground. Its height ish(t) = 10 + v0t − 4.9t2
where h is in meters and t is in seconds.
It hits the ground with a velocity of−25.0
m/s. Findv0
to three sig figs.v0 =
When did it hit the ground? (3 sig figs.)
Okay, so I don't really know how to approach this one. Obviously the derivative is
h'(t)=v(sub)0-9.8t
but I don't see how you can solve with those two variables. If I had to guess, I would assume you would set the equation to where the ball has 0 acceleration and plug in the time to solve for v(sub)0 or something, but I honestly don't know.
Problem #2
The pressure in a cylinder is given by P(t) = 101+(k/t)
where P is in kilopascals (WebAssign abbreviation kPa) and t is in minutes.
Assume thatt ≥ 1
and k is constant.
At the instant when pressure is 114 kPa, it is changing at−0.85
kPa/min.
When does this happen?
What is the pressure whent = 1
minute.
Alright. So, here's what I did on the problem, however I don't know if I was headed down the right path or not.
P(t)=101+ (k/t)
114=101+(k/t)
13=(k/t)
and
P'(t)= -(k/(t^2))
Since we know those have a direct correlation maybe you set them equal to solve for one variable, maybe? Kinda shooting in the dark here...
Problem #3
The electrical potential in a circuit is given byV(t) = 15 − 15e−kt
where V is in volts, t is in seconds, and k is constant.
When t = 0 the rate of change of potential is6.9
V/s. Find the rate of change 3 seconds later.
Find k with correct units. You may find it useful to know the following
FACT: The input to an exponential function must be dimensionless. I.e., it has no units.
k =
Okay. I found the derivative.
V'(t)=15ke^(-kt)
When you plug in 0 for t, obviously the e^(-kt) just turns into 1, and you set it equal to 6.9, so you end up with
6.9=15k
k=.46
Now, .46 could be the correct answer, but I don't know what the units are on it, so I don't know for sure.
Now solving for the first part, when I plug in .46 I got 11.2263217 V/s as the rate of change. However that's wrong, so I'm assuming that k must be wrong.
One last problem that I really just need reassurance on because for whatever reason my professor made it worth a ton of points.
Here's a graph.
Now which of the following graphs would be the derivative of the above graph? I think it would be the last one (graph starts at zero and is the only one that goes above 20, due to the a hint earlier on in the assignment, however I don't understand why the amplitude is greater than the original graph.)
Any responses and help would be appreciated. I have an exam next week and I'm looking to learn the material not just acquire the answers!
Thank you everyone!!!!!!
Problem #1
An object is launched straight upward from a platform above ground. Its height ish(t) = 10 + v0t − 4.9t2
where h is in meters and t is in seconds.
It hits the ground with a velocity of−25.0
m/s. Findv0
to three sig figs.v0 =
When did it hit the ground? (3 sig figs.)
Okay, so I don't really know how to approach this one. Obviously the derivative is
h'(t)=v(sub)0-9.8t
but I don't see how you can solve with those two variables. If I had to guess, I would assume you would set the equation to where the ball has 0 acceleration and plug in the time to solve for v(sub)0 or something, but I honestly don't know.
Problem #2
The pressure in a cylinder is given by P(t) = 101+(k/t)
where P is in kilopascals (WebAssign abbreviation kPa) and t is in minutes.
Assume thatt ≥ 1
and k is constant.
At the instant when pressure is 114 kPa, it is changing at−0.85
kPa/min.
When does this happen?
What is the pressure whent = 1
minute.
Alright. So, here's what I did on the problem, however I don't know if I was headed down the right path or not.
P(t)=101+ (k/t)
114=101+(k/t)
13=(k/t)
and
P'(t)= -(k/(t^2))
Since we know those have a direct correlation maybe you set them equal to solve for one variable, maybe? Kinda shooting in the dark here...
Problem #3
The electrical potential in a circuit is given byV(t) = 15 − 15e−kt
where V is in volts, t is in seconds, and k is constant.
When t = 0 the rate of change of potential is6.9
V/s. Find the rate of change 3 seconds later.
Find k with correct units. You may find it useful to know the following
FACT: The input to an exponential function must be dimensionless. I.e., it has no units.
k =
Okay. I found the derivative.
V'(t)=15ke^(-kt)
When you plug in 0 for t, obviously the e^(-kt) just turns into 1, and you set it equal to 6.9, so you end up with
6.9=15k
k=.46
Now, .46 could be the correct answer, but I don't know what the units are on it, so I don't know for sure.
Now solving for the first part, when I plug in .46 I got 11.2263217 V/s as the rate of change. However that's wrong, so I'm assuming that k must be wrong.
One last problem that I really just need reassurance on because for whatever reason my professor made it worth a ton of points.
Here's a graph.
Now which of the following graphs would be the derivative of the above graph? I think it would be the last one (graph starts at zero and is the only one that goes above 20, due to the a hint earlier on in the assignment, however I don't understand why the amplitude is greater than the original graph.)
Any responses and help would be appreciated. I have an exam next week and I'm looking to learn the material not just acquire the answers!
Thank you everyone!!!!!!