How much time does the mongoose have to react before the black mamba's tail passes the mongoose's nose?

Question

snake length: 2.90m

top speed: 4.90 m/s

In an effort to escape, the snake accelerates past the mongoose at 9.52 m/s^2 from rest.

0.515s for the snake to reach its top speed

snake travels 1.26m in that time

Answer 1

The problem is not quite clear, but here is my interpretation. Assuming the snake's head is next to the mongoose at time = 0, the snake has to travel 2.9 m straight ahead to avoid being eaten by the mongoose. The snake is said to travel 1.26 m in 0.515 s at an acceleration of 9.52 m/s². So, after 0.515 s, the snake is still not out of reach of the mongoose. Also, after 0.515 s, the snake has reached a top speed of 490 m/s, so it has to go 1.64 m (2.9 - 1.26) at 4.90 m/s to get fully past the mongoose. The time to do this is

1.64 m / 4.90 m = 0.335 s.

The total time is get past the mongoose is then 0.515 s + 0.335 s = 0.85 s. The mongoose must react within 0.850 s to catch the snake.