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?

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.