(a) The book decelerates as it moves upwards with magnitude of 6.77 m/s²
(b) The distance traveled by the book before stopping is 0.36 m.
The given parameters;
- mass of the book, m = 1.23 kg
- mass of coffee cup, m₁ = 505 g = 0.505 kg
- initial velocity, u = 2.21 m/s
- coefficient of kinetic friction, μk = 0.221
The vertical component of the force on the book-cup system;

The frictional force on the system;

The horizontal component of the force on the system;
![-mg\ sin(\theta) - F_k = ma\\\\-mg\ sin(\theta) -\mu_kmg \ cos(\theta) = ma\\\\-g\ sin(\theta) -\mu_kg \ cos(\theta) = a\\\\-g[sin(\theta) +\mu_k \ cos(\theta)]= a](https://tex.z-dn.net/?f=-mg%5C%20sin%28%5Ctheta%29%20-%20F_k%20%3D%20ma%5C%5C%5C%5C-mg%5C%20sin%28%5Ctheta%29%20-%5Cmu_kmg%20%5C%20cos%28%5Ctheta%29%20%3D%20ma%5C%5C%5C%5C-g%5C%20sin%28%5Ctheta%29%20-%5Cmu_kg%20%5C%20cos%28%5Ctheta%29%20%3D%20a%5C%5C%5C%5C-g%5Bsin%28%5Ctheta%29%20%2B%5Cmu_k%20%5C%20cos%28%5Ctheta%29%5D%3D%20a)
The acceleration of the book along the slope is calculated as;
![a = -g[sin(\theta) + \mu_k\ cos(\theta)]\\\\a = -9.8[sin(30) + 0.221\times cos(30)]\\\\a = -9.8(0.691)\\\\a = -6.77 \ m/s^2](https://tex.z-dn.net/?f=a%20%3D%20-g%5Bsin%28%5Ctheta%29%20%2B%20%5Cmu_k%5C%20cos%28%5Ctheta%29%5D%5C%5C%5C%5Ca%20%3D%20-9.8%5Bsin%2830%29%20%2B%200.221%5Ctimes%20cos%2830%29%5D%5C%5C%5C%5Ca%20%3D%20-9.8%280.691%29%5C%5C%5C%5Ca%20%3D%20-6.77%20%5C%20m%2Fs%5E2)
Thus, the book decelerates as it moves upwards with magnitude of 6.77 m/s²
(b) The distance traveled by the book before it comes to stop is calculated as;

Thus, the distance traveled by the book before stopping is 0.36 m.
Learn more here:brainly.com/question/16037543