- #1
pete321
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- Homework Statement
- suggest a new initial velocity A of the rocket
- Relevant Equations
- $$\large \int_0^{t_L} A e^{\frac{-t}{\tau}} \text{d}t = A \tau \left( 1- e^{\frac{-t}{\tau}} \right)$$
I am trying to solve the problem below. I have previously calculated from 0 to 4 seconds how far the rocket will travel in each second. I am stuck now as to how to start this problem. I have searched but unable to find the answer. Do i need to rearrange this? A is currently 14 which does not get the rocket to travel 15m in 4 seconds. Once i know how to start this i want to solve on my own so i understand how to complete this.
The integral of the decay curve of the form:
$$Ae^{\frac{-t}{\tau}}$$ This can be expressed as follows:
$$\large \int_0^{t_L} A e^{\frac{-t}{\tau}} \text{d}t = A \tau \left( 1- e^{\frac{-t}{\tau}} \right)$$
$$a = 14$$
$$\tau = 1.6$$
$$ t = 4$$Given this information, suggest a new initial velocity A of the rocket, which will allow the rocket to travel 15m in the same time interval of 0 to t=4.
The integral of the decay curve of the form:
$$Ae^{\frac{-t}{\tau}}$$ This can be expressed as follows:
$$\large \int_0^{t_L} A e^{\frac{-t}{\tau}} \text{d}t = A \tau \left( 1- e^{\frac{-t}{\tau}} \right)$$
$$a = 14$$
$$\tau = 1.6$$
$$ t = 4$$Given this information, suggest a new initial velocity A of the rocket, which will allow the rocket to travel 15m in the same time interval of 0 to t=4.