A 60-kilogram runner has 1920 jouls of kinetic energy. At what speed is she running?

Answer 1

I noticed a lot of down thumbs spread out over all the answers. Either someone is being malicious or, and this is a big OR, someone has recognized that not all the KE is due to linear velocity. There is also angular kinetic energy in the moving arms and legs.

If the arms and legs are equal length L and they are assumed to be rods of mass m each, then I = 4(1/3 m L^2) where m is the mass of each appendage. [See source for the inertia of a rod swung from the end of L.] So we have KE(A) = 1/2 I w^2 = angular kinetic energy where w is the angular velocity of each arm and leg.

As arms and legs move in sync when running, we can say that wL = v, which is the tangential velocity at the hands and feet. v is also the linear velocity at the hips, where the legs join the body.

Thus KE = KE(L) + KE(A) = 1920 kg-(m/sec)^2 = 1/2 Mv^2 + 1/2 I w^2 = 1/2 Mv^2 + 1/2 4(1/3 m L^2) v^2/L^2 = 1/2 v^2 [M + 4/3 m] M = 60 kg, the runner's total mass. From which we find v^2 = 2KE/( M + 4/3 m) = 2*1920/(60 + 4/3 m) and v < 8 mps depending on the mass of each arm and leg. For example, if 4/3 m = 1/6 M, then v^2 = 2*1920/(70) and v = 7.4 mps.

[Recognize a lot of assumptions were made here. But this does show the role angular kinetic energy plays in determining a runner's linear velocity.]

Answer 2

Use the equation .5mV^2 = Kinetic capability so which you desire to remedy for V and depart mass in kg and capability in J V^2 = 1920 J/.5(60kg) V = 8 m/s The J cancel the kg because of the fact J = kg * m^2/s^2 and once you're taking the sq. root it makes it m/s

Answer 3

KE = 1/2*mv^2, or rewrite to:
v = sqrt[2*KE / m]
v = sqrt[2*1920 J / 60kg]
v = 8 m/s

Which is pretty fast, but not as fast as Michael Johnson, who has been clocked at 10.35 m/s

Answer 4

use the formula
Kinetic Energy = 0.5 x mass x (velocity)^2
substitute the numbers in and get the velocity!

Answer 5

1/2m*v^2=1920 -------->m=mass,v=velocity

1/2*60 * v^2=1920

30*v^2=1920

v^2= 64

v=8
she is running at 8m/s