Newtons Second Law Formula Question

[scud0405]

Homework Statement

I've been given a problem that an object falls from a distance of 800 feet with an initial velocity of 4 f/s. Gravity acts on the object, but air resistance can be disregarded. Find the location at time t and find when the object hits the ground.

The Attempt at a Solution

I am confused on the formula. Is the formula that I need to use: $$\frac{dv}{dt} = g - \frac{bv}{m}$$ ?

So with all the numbers plugged in the formula would be:

$$\frac{dv}{dt} = 9.8 - \frac{12}{m}$$ ?


Then I can integrate this and solve to get the answer?

$$\frac{dv}{dt} + \frac{12}{m} = 9.8$$

Mass is not given, so what do I do about the m? I'm completely lost and I just need a hint or two about how to setup the formula.

Thanks.

 

[Mark44]

Why would you use this formula? $$\frac{dv}{dt} = g - \frac{bv}{m}$$
This says that a = g - something. Since you are told you can ignore air resistance, what could possibly be acting on the object to reduce its acceleration?

Isn't dv/dt simply going to be g?

 

[scud0405]

Hmm... it seems it would be, but how would I set-up the formula to determine where the object is at time t? I can't do that with just dv/dt = 9.8, can I?

The at time = 0, velocity is 4, so assuming no air resistance, does that mean it takes 125 seconds to reach the bottom, or does gravity alter its speed?

 

[Mark44]

You have dv/dt = -9.8. (I'm choosing the upward direction to be positive.) How can you solve this differential equation to get v as a function of t? Don't forget that v(0) = -4 ft/sec. You didn't say, but I'm assuming you meant that the initial velocity was downward.

After you get v(t), you can replace v(t) by ds/dt, and do something with that to get the position s as a function of t. This time, don't forget that s(0) = + 800 ft.

 

[scud0405]

Hmm.. so to find v, I would integrate dv/dt, which would give me: v = 9.8t + C? Then, to solve for c, I do 4 = c and that gives me the equation for time which is v(t) = 9.8t + 4?

Is this correct so far, or what do I need to reconsider?

 

[Mark44]

No, not correct, but you have the basic idea. You need to pay attention to the signs of things, though. The way I have set it up, down is negative and up is positive.

 

[scud0405]

Okay, so would it just be v(t)= -9.8t + 4 and then I substitute v(t) with ds/dt?

 

[Mark44]

No, it's partly wrong. Which direction is the initial velocity? Reread post #4 carefully.

 

[scud0405]

Oh, yeah, whoops. It is: v(t)= -9.8t - 4. Okay, now I make the problem:

ds/dt = -9.8t - 4

Am I on the right track now?

I am suppose to integrate next, correct?

 

[Mark44]

Yes and yes.