Solve Velocity and Time Homework: Tr=3

[adoado]

Homework Statement

Boxes are placed on a chute at a uniform rate of time T_r and slide down the chute with uniform acceleration. Knowing that as any box B is released, the preceeding box A is 6m down the chute; 1 second later there is a 10m distance between them. Determine the value of T_r

Homework Equations

The Attempt at a Solution

As x = 0.5at²
6 = 0.5a(T_r)²

I found a to be (change in y) / (change in x) = 4 m/sec²

So, $$\sqrt{6/(0.5*0.4)}$$ = 3^(0.5) = T_r

But the answer is plain old 3...

Any advice appreciated :)
Adrian

 

[anathema]

,

Great job on tackling this problem! Your approach is definitely on the right track. However, there are a few things to consider in your solution:

1. Units: Make sure to keep track of your units throughout your solution. In this case, you are using meters and seconds, so your final answer for Tr should also have units of seconds.

2. Simplification: In your equation, you have a factor of 0.5 on both sides. This can be simplified to give you a simpler expression for Tr.

3. Substitution: You have correctly found the value of a, but you have not substituted it back into your equation to solve for Tr. This is why you are getting a different answer than expected.

Here is a step-by-step solution for this problem:

1. Start with the given information:
- Box A is 6m down the chute when box B is released
- 1 second later, there is a 10m distance between them

2. Use the equation x = 0.5at^2 to relate the distance and time for each box:
- For box A: x = 0.5a(1)^2 = 0.5a
- For box B: x = 0.5a(Tr)^2

3. Use the given information to set up an equation:
- Box B has traveled 10m in Tr seconds, so we can write: 10 = 0.5a(Tr)^2
- Box A has traveled 6m in (Tr-1) seconds, so we can write: 6 = 0.5a(Tr-1)^2

4. Simplify the equations:
- 10 = 0.5a(Tr)^2
- 6 = 0.5a(Tr^2 - 2Tr + 1)
- 6 = 0.5aTr^2 - aTr + 0.5a

5. Substitute 4m/s^2 for a (as you correctly calculated):
- 10 = 0.5(4)(Tr)^2
- 6 = 0.5(4)(Tr^2 - 2Tr + 1)
- 6 = 2Tr^2 - 4Tr + 2

6. Solve for Tr:
- 10 = 2Tr^2
-