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Answer :
The mongoose has 0.769 seconds to react before the black mamba's tail passes its nose, calculated using the kinematic equation for distance in terms of acceleration and time.
To find out how much time the mongoose has to react before the black mamba's tail passes by, we need to consider the snake's acceleration and the time it takes for the entire length of the snake to pass the mongoose. The snake starts from rest (initial velocity, u, is 0 m/s) and accelerates at 9.46 m/s². To calculate the total time (t) it takes for the snake's 2.80 m body to pass by, we use the formula for distance (s) in terms of acceleration (a) and time, which is s = ut + 0.5at2.
Plugging in the values gives us:
2.80 m = 0 m/s + 0.5 (9.46 m/s²){t²}
2.80 m = 4.73 m/s²{t²}
t = 2.80 m / 4.73 m/s²
t = 0.592 m²/s²
t =√ (0.592 m²/s²)
t = 0.769 seconds (approximately).
Therefore, the mongoose has about 0.769 seconds to react before the black mamba's tail passes its nose.
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Rewritten by : Barada
The length of the black mamba snake is 2.80 m and has a top speed of 4.80 m/s. Suppose a mongoose and a black mamba find themselves nose to nose. In an effort to escape, the snake accelerates past the mongoose at 9.46 m/s² from rest.
Time taken by the black mamba to accelerate past the mongoose can be calculated using the following kinematic equation: V² = U² + 2as
WhereV = Final
velocity = 4.80 m/s
U = Initial velocity = 0 (from rest)
a = Acceleration = 9.46 m/s²s
= Distance covered by the black mambaLet's calculate s: [tex]s = V² - U² / 2as = 4.80² / 2 × 9.46= 0.48 m[/tex]
Now, the total distance covered by the black mamba before its tail passes the mongoose's nose is: Distance = Length of black mamba + Distance covered by black mamba Distance = 2.80 + 0.48
= 3.28 m Time taken by the black mamba to cover this distance is: Time = Distance / Speed Time = 3.28 / 4.80= 0.6833 seconds, the mongoose has 0.6833 seconds to react before the black mamba's tail passes the mongoose's nose.
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