A boulder flies through the air at 14.5 m/s with kinetic energy 310 J.
What's its mass?
What's the boulder's kinetic energy if its speed doubles?
What's the boulder's kinetic energy if its speed is halved?
KE = 1/2 mv^2, solve for m
Once you've found m use the other two v's, same eq.
thank you
2.95 kg
1240 J
77.5 J
To find the mass of the boulder, we can use the equation for kinetic energy:
Kinetic Energy (KE) = (1/2) * mass * velocity^2
We are given the kinetic energy of the boulder as 310 J and the velocity as 14.5 m/s. Plugging these values into the equation, we can solve for the mass:
310 = (1/2) * mass * (14.5)^2
To simplify the calculation, we first square the velocity:
310 = (1/2) * mass * 210.25
Now, we isolate the mass variable by dividing both sides of the equation by 210.25:
mass = 310 / (0.5 * 210.25)
mass ≈ 2.325 kg
Therefore, the mass of the boulder is approximately 2.325 kg.
To find the boulder's kinetic energy if its speed doubles, we need to calculate the new velocity.
Given that the original velocity is 14.5 m/s, if the speed doubles, the new velocity would be 2 * 14.5 = 29 m/s.
Using the same equation for kinetic energy, we can now calculate the new kinetic energy:
New KE = (1/2) * mass * (new velocity)^2
Plugging in the values, we have:
New KE = (1/2) * 2.325 * (29)^2
New KE ≈ 1214.3625 J
Therefore, the boulder's kinetic energy when its speed doubles is approximately 1214.3625 J.
Finally, to find the boulder's kinetic energy if its speed is halved, we need to calculate the new velocity again.
Given that the original velocity is 14.5 m/s, if the speed is halved, the new velocity would be 14.5 / 2 = 7.25 m/s.
Using the same equation for kinetic energy, we can calculate the new kinetic energy:
New KE = (1/2) * mass * (new velocity)^2
Plugging in the values, we have:
New KE = (1/2) * 2.325 * (7.25)^2
New KE ≈ 90.30625 J
Therefore, the boulder's kinetic energy when its speed is halved is approximately 90.30625 J.