Given data:
Initial speed (u) = 10 m/s
Coefficient of kinetic friction (μ) = 0.10

Calculating the force of friction:
The force of friction (F) can be calculated using the formula F = μN, where N is the normal force.
Since the block is moving horizontally, the normal force (N) is equal to the weight of the block (mg).

The weight of the block (W) can be calculated using the formula W = mg, where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s²).

Calculating the distance traveled:
The acceleration of the block (a) can be calculated using the formula a = F/m, where m is the mass of the block.

Since the block is projected horizontally, there is no vertical acceleration. Thus, the horizontal distance traveled (s) can be calculated using the formula s = ut + (1/2)at², where t is the time taken.

Calculating the time taken:
To find the time taken (t), we need to use the equation of motion v = u + at, where v is the final velocity.

Since the block comes to rest, the final velocity (v) is 0 m/s.

Calculating the mass of the block:
To calculate the mass of the block, we need more information. If the mass is given, it can be directly used in the calculations. If not, we can use the weight of the block (W) and the acceleration due to gravity (g) to find the mass using the formula W = mg.

Summary:
To find the distance traveled by the block before coming to rest, we need to calculate the force of friction, the acceleration of the block, the time taken, and finally, the distance traveled. However, the mass of the block is required for these calculations. Once the mass is known, the above formulas can be used to find the distance traveled.

50m