Bobbo starts swimming at $2$ feet/s across a $100$ foot wide river with a current of $5$ feet/s.  Bobbo doesn’t know that there is a waterfall $175$ feet from where he entered the river. He realizes his predicament midway across the river. What is the minimum speed that Bobbo must increase to make it to the other side of the river safely?
1. Bobbo starts swimming at a speed of $2$ feet per second across a $100$ foot wide river. The current of the river is $5$ feet per second.
2. Bobbo realizes his predicament midway across the river, which means he has swum $50$ feet. The time taken to swim $50$ feet at $2$ feet per second is:
   \[
   \frac{50 \text{ feet}}{2 \text{ feet/second}} = 25 \text{ seconds}
   \]
3. During these $25$ seconds, the current has swept Bobbo downstream. The distance swept downstream is:
   \[
   25 \text{ seconds} \times 5 \text{ feet/second} = 125 \text{ feet}
   \]
4. The waterfall is $175$ feet from where Bobbo entered the river. Therefore, the remaining distance downstream to the waterfall is:
   \[
   175 \text{ feet} - 125 \text{ feet} = 50 \text{ feet}
   \]
5. Bobbo needs to cross the remaining $50$ feet of the river before being swept the remaining $50$ feet downstream. The time it takes for the current to sweep him $50$ feet downstream is:
   \[
   \frac{50 \text{ feet}}{5 \text{ feet/second}} = 10 \text{ seconds}
   \]
6. To cross the remaining $50$ feet of the river in $10$ seconds, Bobbo must swim at a speed of:
   \[
   \frac{50 \text{ feet}}{10 \text{ seconds}} = 5 \text{ feet/second}
   \]
7. Bobbo's initial swimming speed is $2$ feet per second. Therefore, the increase in speed required is:
   \[
   5 \text{ feet/second} - 2 \text{ feet/second} = 3 \text{ feet/second}
   \]

The final answer is $\boxed{3}$ feet per second.