a runner runs 100.0 m in 9.85 seconds. If he has a kinetic energy of 3400.0 J what is the mass?
KE = 1/2*m*v^2
To find the mass of the runner, we can use the formula for kinetic energy:
KE = (1/2)mv^2
where KE is the kinetic energy, m is the mass, and v is the velocity.
First, let's rearrange the formula to solve for mass:
m = (2KE) / v^2
Given that the kinetic energy is 3400.0 J, the velocity is the distance divided by the time:
v = distance / time
Substituting the values, we have:
v = 100.0 m / 9.85 s
Now we can calculate the velocity:
v = 10.152 m/s
Plugging this back into the formula, we can calculate the mass:
m = (2 * 3400.0 J) / (10.152 m/s)^2
Simplifying:
m = 6800.0 J / (103.05 m^2/s^2)
m = 66.08 kg (rounded to two decimal places)
Therefore, the mass of the runner is approximately 66.08 kg.