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?
Ke = (1/2) m v^2
if v = 2 v
Ke = (1/2) m (2v)^2 = (1/2) m v^2 * 4
so
new Ke = 4 * original Ke
4 * 5.1 = 20.4 J
A.
To predict the hawk's kinetic energy at the end of the chase, we can use the principle of conservation of energy. According to this principle, the total mechanical energy of a system remains constant, assuming there are no external forces or energy losses.
Given that the hawk's kinetic energy at the beginning of the chase is 5.1 Joules and the hawk doubles its speed, we can assume that there are no external forces acting on the hawk-sparring system.
Since kinetic energy is directly proportional to the square of the speed, if the speed doubles, the kinetic energy will be four times greater.
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 Joules * 4 = 20.4 Joules.
To predict the kinetic energy of the hawk at the end of the chase, we'll need to consider the relationship between kinetic energy and speed.
The formula for kinetic energy is:
KE = 1/2 * m * v^2
Where:
KE is the kinetic energy,
m is the mass of the object, and
v is the velocity or speed of the object.
In this case, since we are comparing the hawk's kinetic energy before and after the chase, we can assume that the mass of the hawk remains constant.
Therefore, we only need to consider the change in speed of the hawk. The problem states that the hawk doubles its speed. Let's assume the initial speed of the hawk is v, so the final speed would be 2v.
Since kinetic energy is proportional to the square of the speed, if the speed doubles, the kinetic energy will be four times the initial value. It means that the kinetic energy at the end of the chase is four times the initial kinetic energy.
To calculate the final kinetic energy, we can use this relationship. Given that the initial kinetic energy was 5.1 Joules, we can multiply it by 4 to get the best prediction for the final kinetic energy.
Final Kinetic Energy = Initial Kinetic Energy * 4
Final Kinetic Energy = 5.1 J * 4
Final Kinetic Energy = 20.4 Joules
Therefore, the best prediction for the hawk's kinetic energy at the end of the chase is 20.4 Joules.