Question

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?

Answer 1

Answer:

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.