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24 March, 22:44

A bomb falls with velocity v (t) = C (1-e-kt), where C and k are constants. What is the terminal velocity of the bomb? That is, what is the maximum valocity the bomb can reach regardless of the height of the bomber?

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  1. 25 March, 02:32
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    The terminal velocity is equal to C.

    Explanation:

    Making the assumption that k and t are positive, we then have that - kt is negative. The value of e^ (-kt) will be equal to 1 / (e^ (kt))

    If t increases, e^ (kt) will increase exponentially and its reciprocal 1 / (e^ (kt)) will approach zero.

    So, we have:

    v (t) = C * (1-0)

    v (t) = C * (1)

    v (t) = C

    Therefore, C is the terminal velocity.
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