Question

A 5000 kg rocket is set for vertical firing. The exhaust speed is 800ms-1 . To give an initial uoward acceleration of 20ms-2 the amount of gas ejected per second to supply the needed thrust will be

Answer 1

The gas ejected per second to get the needed thrust is 186.25 kg/s.

Explanation:

The concept of thrust comes from Newton’s third law. The thrust is the upward force to push some object in the upward direction. Thrust is equal to the amount of material ejected to push the object upward.

So, thrust can be written mathematically,

$\text{Thrust}=v \frac{d m}{d t}$

Here v is the exhaust speed and m is the amount of gas ejected out.

The upward force can also be found as,

$F=m(a+g)$

Where,

a is the acceleration of rocket

g is the acceleration due to gravity

$\therefore \text { Thrust }=F$

$v \frac{d m}{d t}=m(a+g) \rightarrow(1)$

The data given in the question are as follows

m = 5000 kg; v = 800 ms-1; a = 20 ms-2; and g = 9.8 ms-2 (known value).

Substituting these values in eqn (1), we get,

$800 \times \frac{d m}{d t}=5000 \times(20+9.8)$

$\frac{d m}{d t}=\frac{5000 \times(20+9.8)}{800}$

The amount of gas ejected for providing thrust  

$\therefore \frac{d m}{d t}=186.25 \ \mathrm{kg} / \mathrm{s}$

Answer 2

Answer:

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