Question:
A 25ft ladder is leaning against a vertical wall. The bottom of the ladder is pulled horizontally away from the wall at 3 ft/sec. How fast is the top of the ladder sliding down the wall when the bottom of the ladder is 15ft away from the wall?
Answer:
1a)
![](https://static.wixstatic.com/media/20c892_9b6c4751f1aa4b0b89dde6228d65e32b~mv2.png/v1/fill/w_81,h_70,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_9b6c4751f1aa4b0b89dde6228d65e32b~mv2.png)
From the question we know that when x = 15ft, y = 20ft and dx/dt = 3ft/sec. We can input this data into our derived formula.
![](https://static.wixstatic.com/media/20c892_b1d32ed96016476c9ab64bf1cc044bbf~mv2.png/v1/fill/w_77,h_14,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_b1d32ed96016476c9ab64bf1cc044bbf~mv2.png)
The top of the ladder is sliding down the wall at the rate of 9/4 ft/sec.