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Answer :
Final Answer:
The mongoose has approximately 0.525 seconds to react before the black mamba's tail passes its nose.
Explanation:
To determine the time the mongoose has to react, we can use the following equations of motion:
1. The distance covered by the black mamba as it accelerates from rest can be calculated using the equation:
[tex]\[s = ut + \frac{1}{2}at^2\][/tex]
where:
s = distance covered (which is the length of the snake, 2.60 m)
u = initial velocity (0 m/s, as the snake starts from rest)
a = acceleration (8.75 m/s²)
t = time
2. We want to find the time it takes for the snake to accelerate to its top speed, so we can use the equation:
[tex]\[v = u + at\][/tex]
where:
v = final velocity (4.60 m/s, the snake's top speed)
u = initial velocity (0 m/s)
a = acceleration (8.75 m/s²)
t = time
Rearranging the second equation to solve for time, we get:
[tex]\[t = \frac{v}{a}\][/tex]
Substituting the values, we find:
[tex]\[t = \frac{4.60\, m/s}{8.75\, m/s^2} \approx 0.525\, s\][/tex]
So, the snake takes approximately 0.525 seconds to accelerate to its top speed. During this time, the mongoose must react. Since the snake has a head start, the mongoose has approximately 0.525 seconds to react before the snake's tail passes its nose.
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