Question

8. (a) Suppose an object moving supersonically obeys the following motion equation: Find the limiting velocity in terms of m, p, and k (b) Suppose the flight velocity of Kara Zor-El (also known as Supergirl), in thousand miles per second, is described by the equation below. Solve the equation. You may leave your answer in an implicit form. v 243-3v4 Also find her maximum/limiting velocity.
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Answer #1

Given is:-

mv' = p - kv^4

now,

part -a

When object has limiting velocity then  dv t/=-=0 dt ひ

thus

m(0) = p-ku,4

or

지4) This is the limiting velocity.

Part-b

The equation of flight velocity of super girl

243-31,4 ,

dv U) 243-3u4 dt

or

dv (243-37) = dt

Integrating both sides we get

4-81

3 3100 dv

which gives us

324

Part-c

For maximum limiting velocity v'=0

thus

0- 243 -3u

which gives us

v = (rac{243}{3})^{rac{1}{4}}

which gives us

3 thousand miles per second

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