Your approach is mostly correct, but there is a mistake in calculating the frictional force. Let's go over the correct steps again.
1. Break the force F into horizontal and vertical components:
- The horizontal component F_horizontal = F * cos(theta) = 18 N * cos(45°) = 12.7 N
- The vertical component F_vertical = F * sin(theta) = 18 N * sin(45°) = 12.7 N
2. Calculate the net force acting on the block in the horizontal direction:
- F_net(horizontal) = F_horizontal - friction = 12.7 N - friction
3. Calculate the frictional force:
- The normal force N is equal to the weight of the block, N = m * g = 3 kg * 9.8 m/s^2 = 29.4 N
- friction = coefficient of kinetic friction * N = 0.25 * 29.4 N = 7.35 N
4. Substitute the frictional force value into the net force equation:
- F_net(horizontal) = 12.7 N - 7.35 N = 5.35 N
5. Calculate the acceleration of the block in the horizontal direction:
- F_net(horizontal) = m * a
- 5.35 N = 3 kg * a
- a = 5.35 N / 3 kg = 1.78 m/s^2
Therefore, the magnitude of the frictional force on the block from the floor is 7.35 N, and the magnitude of the block's acceleration is 1.78 m/s^2.
Note: Ensure that you use the correct signs for the components of forces and angles in your calculations. Also, double-check your trigonometric calculations using the appropriate units for angles (degrees or radians).