## Related questions with answers

The impulse J due to a force F is the product of the force times the amount of time t for which the force acts. When the force varies over time, $J=\int_{t_{1}}^{t_{2}} F(t) d t$. We can model the force acting on a rocket during launch by an exponential function $F(t)=A e^{b t}$, where A and b are constants that depend on the characteristics of the engine. At the instant lift-oft occurs (t=0), the force must equal the weight of the rocket. (a) Suppose the rocket weighs 25,000 N (a mass of about 2500 kg or a weight of 5500 lb), and 30 seconds after lift-off the force acting on the rocket equals twice the weight of the rocket. Find A and b. (b) Find the impulse delivered to the rocket during the first 30 seconds after the launch.

Solution

VerifiedWe are given the following equations:

$J = \int_{t_1}^{t_2} F(t) \ dt \quad \quad F(t) = Ae^{bt} \quad \quad F(0) = 25 000$

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