A hawk is chasing a sparrow. At the beginning of the chase, the hawk’s kinetic energy is 5.1 Joules. At the end of the chase, the hawk doubles its speed. What is the best prediction for its kinetic energy at the end of the chase?(1 point) Responses 20.4 J 20.4 J 5.1 J 5.1 J 2.55 J 2.55 J 10.2 J
The kinetic energy of an object is directly proportional to the square of its velocity. Since the hawk doubles its speed, its kinetic energy at the end of the chase will be four times its initial kinetic energy. Therefore, the best prediction for its kinetic energy at the end of the chase is 20.4 J.
To find the best prediction for the hawk's kinetic energy at the end of the chase, we need to determine the relationship between kinetic energy and speed.
Kinetic energy is given by the equation: KE = (1/2)mv^2, where KE represents kinetic energy, m represents mass, and v represents velocity or speed.
Since only the speed of the hawk is given, we can assume that the mass remains constant. Therefore, we can compare the kinetic energy at the beginning and the end of the chase using the ratio of their speeds squared.
Given that the hawk doubles its speed, we can calculate the ratio:
(2v)^2 / v^2 = 4v^2 / v^2 = 4
This means that the kinetic energy at the end of the chase will be 4 times the initial value.
Therefore, the best prediction for the hawk's kinetic energy at the end of the chase is 4 times the initial kinetic energy:
5.1 J * 4 = 20.4 J
Hence, the correct answer is 20.4 J.
To predict the kinetic energy at the end of the chase, we need to consider the relationship between kinetic energy and speed.
The formula for kinetic energy is given by:
Kinetic Energy = 1/2 * mass * velocity^2
Since the mass of the hawk remains constant during the chase, we can disregard it and focus on the change in velocity.
We are given that at the beginning of the chase, the hawk's kinetic energy is 5.1 Joules.
According to the question, at the end of the chase, the hawk doubles its speed.
We can use this information to find the relationship between the initial speed (v1) and the final speed (v2) using the given kinetic energy values.
Using the equation for kinetic energy, we can set up the following relationship:
1/2 * v1^2 = 5.1 J
Since the hawk doubles its speed, we can write the relationship as:
1/2 * (2*v1)^2 = kinetic energy at the end of the chase
By simplifying the equation, we get:
1/2 * 4 * v1^2 = kinetic energy at the end of the chase
2 * v1^2 = kinetic energy at the end of the chase
We can substitute the value of v1^2 from the initial kinetic energy of 5.1 J:
2 * 5.1 J = kinetic energy at the end of the chase
Calculating the value gives us:
10.2 J
Therefore, the best prediction for the hawk's kinetic energy at the end of the chase is 10.2 Joules.
So the correct answer is 10.2 J.