A black mamba snake has a length of 4.3 m and a top speed of 8.9 m/s! Suppose a mongoose and a black mamba find themselves nose to nose. In an effort to escape, the snake accelerates at 20 m/s2 from rest.
(a) How much time does it take for the snake to reach its top speed?
(b) How far does the snake travel in that time?(c) How much reaction time does the mongoose have before the tail of the mamba snake passes by?
2.30
a. V = a*t = 8.9 m/s.
20*t = 8.9.
t = 0.445 s.
b. d = 0.5a*t^2.
c. d = 0.5a*t^2.
d = 4.3 m.
a = 20 m/s^2.
Solve for t.
(a) To find the time it takes for the snake to reach its top speed, we can use the equation:
Speed = Initial Speed + Acceleration * Time
Let's assume the initial speed of the snake is 0 m/s.
So the equation becomes:
8.9 m/s = 0 m/s + 20 m/s^2 * Time
Simplifying the equation, we have:
20 m/s^2 * Time = 8.9 m/s
Dividing both sides by 20 m/s^2, we get:
Time = 8.9 m/s / 20 m/s^2
Time = 0.445 s
Therefore, it takes the snake approximately 0.445 seconds to reach its top speed.
(b) To find the distance the snake travels in that time, we can use the equation:
Distance = Initial Speed * Time + (1/2) * Acceleration * Time^2
Since the initial speed is 0 m/s, the equation simplifies to:
Distance = (1/2) * Acceleration * Time^2
Plugging in the values, we have:
Distance = (1/2) * 20 m/s^2 * (0.445 s)^2
Distance = 0.5 * 20 m/s^2 * 0.198 m^2/s^2
Distance = 1.98 m
Therefore, the snake travels approximately 1.98 meters in that time.
(c) To find the reaction time of the mongoose before the tail of the snake passes by, we need to know the length of the snake.
Given that the length of the snake is 4.3 meters, we can use the equation:
Reaction Time = Distance / Speed
Plugging in the values, we have:
Reaction Time = 4.3 m / 8.9 m/s
Reaction Time = 0.483 s
Therefore, the mongoose has approximately 0.483 seconds of reaction time before the tail of the mamba snake passes by.
To answer these questions, we need to understand the basic principles of motion and use the equations of motion.
Let's break down each question and explain how to solve them:
(a) How much time does it take for the snake to reach its top speed?
To determine the time it takes for the snake to reach its top speed, we can use the equation of motion:
v = u + at
Where:
- v is the final velocity (top speed) of the snake,
- u is the initial velocity (0 m/s, as the snake starts from rest),
- a is the acceleration of the snake (20 m/s^2),
- t is the time it takes to reach the top speed.
Rearranging the equation, we get:
t = (v - u) / a
Substituting the given values, we have:
t = (8.9 m/s - 0) / 20 m/s^2
Simplifying the expression, we find:
t = 0.445 seconds
Therefore, it takes the snake approximately 0.445 seconds to reach its top speed.
(b) How far does the snake travel in that time?
To calculate the distance travelled by the snake during that time, we can use the equation of motion:
s = ut + (1/2)at^2
Where:
- s is the distance travelled by the snake,
- u is the initial velocity (0 m/s),
- a is the acceleration (20 m/s^2),
- t is the time taken (0.445 seconds).
Substituting the given values, we get:
s = 0(0.445) + (1/2)(20)(0.445)^2
Simplifying the expression, we find:
s = 0.198 m
Therefore, the snake travels approximately 0.198 meters in that time.
(c) How much reaction time does the mongoose have before the tail of the mamba snake passes by?
To find the reaction time of the mongoose, we need to determine the time it takes for the snake's tail to pass by. This is equal to the time it takes for the snake to reach its top speed (as calculated in part a). Let's assume that the length of the snake is measured from the head to the tail.
So, the time it takes for the tail of the snake to pass by is approximately 0.445 seconds. This gives the mongoose a reaction time of 0.445 seconds.
It's important to note that these calculations assume constant acceleration for the snake and neglect any other factors, such as the reaction time of the mongoose. In reality, these values may vary.