1. Well, if the boy is pushing the car backwards, he's definitely working against the car's motion. So, we can say the work done by the boy is negative. But let's calculate the actual work done. Work is equal to force times distance, so the work done by the boy is 10N * 3.0m = 30N•m. So, the correct answer is d) 30 N•m. That boy sure is working hard!
2. Let's see, if the kinetic energy of the ball is 40J, we can use the formula for kinetic energy: KE = (1/2)mv^2, where KE is kinetic energy, m is mass, and v is velocity. Rearranging the formula, we get v = sqrt(2KE/m). Plugging in the values, we get v = sqrt(2 * 40J / 5.0kg) = sqrt(16m^2/s^2) = 4m/s. So, the correct answer is b) 4 m/s. That's one speedy ball!
3. To raise a child onto a counter top, we need to overcome the force of gravity acting on the child. The potential energy of an object is given by PE = mgh, where PE is potential energy, m is mass, g is acceleration due to gravity, and h is height. Plugging in the values, we get PE = 20kg * 9.8m/s^2 * 1.25m = 245J. So, the correct answer is c) 245 J. That's a lot of energy for a child to get on the counter!
4. When mechanical energy is conserved, it means that the sum of the kinetic energy and gravitational potential energy remains constant. So, the correct answer is a) the sum of the kinetic energy and gravitational potential energy remains constant. Just like how I conserve my energy by not doing any physical work!
5. If the cyclist has 4,100J of energy, it could be a combination of kinetic energy and potential energy. But since there's no mention of any height, let's assume it's all kinetic energy. The formula for kinetic energy is KE = (1/2)mv^2. Rearranging the formula, we get v = sqrt(2KE/m). Plugging in the values, we get v = sqrt(2 * 4,100J / 82kg) = sqrt(100m^2/s^2) = 10m/s. So, the correct answer is d) 10 m/s. That cyclist is on a roll!