The student claims that about Jock 3.0 m would have fewer than 96 J of kinetic energy upon a hitting the ground is she correct?
To determine if the student is correct, we need to utilize the equation for kinetic energy:
Kinetic energy (KE) = (1/2) * mass * velocity^2
Since we are given the height (3.0 m) and not the velocity, we need to find the velocity first using the equation for gravitational potential energy:
Potential energy (PE) = mass * gravity * height
Since gravitational potential energy is converted to kinetic energy as the object falls, we can equate the two equations:
PE = KE
mass * gravity * height = (1/2) * mass * velocity^2
height = (1/2) * velocity^2 / gravity
After rearranging the equation, we find:
velocity = √(2 * gravity * height)
Now, let's calculate the velocity:
velocity = √(2 * 9.8 m/s^2 * 3.0 m)
= √(58.8 m^2/s^2)
= 7.67 m/s
Now, let's calculate the kinetic energy at this velocity:
KE = (1/2) * mass * velocity^2
Since we don't have the mass of Jock, we cannot determine the exact kinetic energy. Thus, we cannot say for certain if the student's claim is correct without additional information.
To determine if the student's claim is correct, we need to apply the principles of physics related to kinetic energy.
The formula for calculating the kinetic energy of an object is given by:
Kinetic Energy (KE) = 0.5 * mass * velocity^2
We know that the student claims about Jock 3.0 m, so let's assume Jock refers to an object or a person falling from a height of 3.0 meters.
To calculate the velocity of Jock when hitting the ground, we can use another formula related to free fall motion:
Final Velocity (Vf) = √(2 * acceleration * distance)
The acceleration due to gravity on Earth is approximately 9.8 m/s^2.
Let's substitute the given values into the formula and calculate the final velocity:
Vf = √(2 * 9.8 m/s^2 * 3.0 m)
Vf = √(58.8 m^2/s^2)
Vf ≈ 7.67 m/s
Now, we can substitute the final velocity value into the kinetic energy formula to find the kinetic energy of Jock when hitting the ground:
KE = 0.5 * mass * velocity^2
Since we don't have the mass of Jock given, we cannot calculate the kinetic energy exactly. However, we can make a general conclusion:
Given the height of 3.0 meters, and assuming Jock falls freely under the influence of gravity, the student's claim that Jock would have fewer than 96 Joules of kinetic energy upon hitting the ground is likely to be correct.