a 3.00kg object has a velocity [6.00i-2.00j]m/s. what is the kinetic energy at this moment.
6 m/s to the east and 2 m/s to the south
well what is the speed squared, v^2 ?
v^2 = 6^2 + 2^2 = 36 + 4 = 40
so
Ke = (1/2) m v^2 = (1/2) 3 * 40 = 60 Joules
To calculate the kinetic energy of an object, we use the formula:
Kinetic Energy (KE) = (1/2) * mass * velocity^2
Here's how to calculate the kinetic energy at this moment:
1. First, find the magnitude of the velocity vector. The magnitude of a vector can be found using the Pythagorean theorem:
magnitude = sqrt((velocity_x)^2 + (velocity_y)^2)
In this case, velocity_x = 6.00 m/s and velocity_y = -2.00 m/s.
Therefore, the magnitude of the velocity vector is:
magnitude = sqrt((6.00)^2 + (-2.00)^2) = sqrt(36.00 + 4.00) = sqrt(40.00) = 6.32 m/s
2. Now that we have the magnitude of the velocity vector, we can calculate the kinetic energy using the formula:
KE = (1/2) * mass * velocity^2
Given that the mass of the object is 3.00 kg and the magnitude of the velocity is 6.32 m/s, we can substitute these values into the formula:
KE = (1/2) * 3.00 kg * (6.32 m/s)^2
Solve the equation:
KE = (1/2) * 3.00 * (6.32)^2
KE = 0.5 * 3.00 * 39.94
KE = 59.91 Joules
So, the kinetic energy of the object at this moment is 59.91 Joules.