- Percentage error in mass measurement = 2%
- Percentage error in speed measurement = 3%


- The error in kinetic energy obtained by measuring mass and speed.



The formula for kinetic energy (KE) is given by:

KE = (1/2)mv²

where:
- KE is the kinetic energy,
- m is the mass,
- v is the speed.


The error in kinetic energy can be calculated using the formula for relative error. The relative error is given by:

Relative error = (error in quantity) / (actual quantity)


Given that the percentage error in mass measurement is 2%, the error in mass can be calculated as:

Error in mass = (2/100) * mass


Given that the percentage error in speed measurement is 3%, the error in speed can be calculated as:

Error in speed = (3/100) * speed


To find the error in kinetic energy, we need to calculate the derivative of the kinetic energy formula with respect to both mass and speed:

dKE/dm = (1/2) * v²
dKE/dv = m * v

Using the formula for relative error, the error in kinetic energy can be calculated as:

Error in kinetic energy = [(dKE/dm) * (error in mass)] + [(dKE/dv) * (error in speed)]

Substituting the calculated values:

Error in kinetic energy = [(1/2) * v² * (2/100) * mass] + [m * v * (3/100) * speed]
Error in kinetic energy = (1/100) * (v² * mass + 3 * m * v * speed)


To find the percentage error, we need to divide the error in kinetic energy by the actual kinetic energy and multiply by 100:

Percentage error = (Error in kinetic energy / Actual kinetic energy) * 100

Since we do not know the actual kinetic energy, we cannot calculate the exact percentage error. However, we can simplify the equation for the error in kinetic energy:

Percentage error = (1/100) * (v² * mass + 3 * m * v * speed) / Actual kinetic energy * 100

From the equation, we can see that the percentage error depends on the actual kinetic energy. Without knowing the actual kinetic energy, we cannot determine the exact percentage error. Therefore, the answer cannot be determined without additional information.