Final answer:
Using the conservation of energy, the potential energy from which the book fell equals the kinetic energy when it hits the ground. The height calculated is 0.8 meters.
Step-by-step explanation:
The question involves using the principles of energy conservation, specifically the conversion of potential energy to kinetic energy, to determine the height from which a book falls. To find the height from which a 3 kg book falls when it lands with a speed of 4.0 m/s, you can use the formula for gravitational potential energy, PE = mgh, and the formula for kinetic energy, KE = 0.5 * mv2. Since energy is conserved, the potential energy at the height it fell from will equal the kinetic energy when the book hits the ground.
Setting these equal to one another gives us mgh = 0.5 * mv2. By cancelling out the mass (m) since it appears on both sides, and plugging in the values for g (9.8 m/s2), and v (4.0 m/s), we can solve for h (the height) as follows: h = (0.5 * v2) / g = (0.5 * 4.02) / 9.8 = 0.8163 meters. The closest answer rounded to the nearest tenth is 0.8 m, which is option D.