At what speed would a 50kg person have to run to have the same kinetic energy as a 1000kg auto traveling at 100 km/h?
Help ASAP please!! Show work step by step along with the equation
V = 100km/h = 100,000m/3600s = 27.78 m/s.
KE = 0.5M*V^2 = 500 * 27.78^2 = 385,802 J. = KE of the auto.
0.5M*V^2 = 385,802.
25*V^2 = 385,802, V = ?.
124.2 m/s
To find the speed at which a 50kg person would have the same kinetic energy as a 1000kg auto traveling at 100 km/h, we can use the equation for kinetic energy:
Kinetic energy = (1/2) * mass * velocity^2
First, let's find the kinetic energy of the auto. The mass of the auto is given as 1000 kg, and the velocity is given as 100 km/h. We need to convert the velocity from km/h to m/s, so:
Velocity (m/s) = 100 km/h * (1000 m/1 km) * (1 h/3600 s) = (100000/3600) m/s = 27.78 m/s
Now we can calculate the kinetic energy of the auto:
Kinetic energy of auto = (1/2) * 1000 kg * (27.78 m/s)^2
Next, let's find the speed at which the 50kg person would have the same kinetic energy. We'll use the same equation:
Kinetic energy of person = (1/2) * 50 kg * velocity_person^2
We want to find the velocity_person, so we'll set the two kinetic energies equal to each other:
(1/2) * 1000 kg * (27.78 m/s)^2 = (1/2) * 50 kg * velocity_person^2
Simplifying and solving for velocity_person:
1000 * 27.78^2 = 50 * velocity_person^2
velocity_person^2 = (1000 * 27.78^2) / 50
velocity_person^2 ≈ 1532.72
velocity_person ≈ √1532.72
velocity_person ≈ 39.15 m/s
Therefore, the 50kg person would have to run at a speed of approximately 39.15 m/s to have the same kinetic energy as a 1000kg auto traveling at 100 km/h.