Final answer:
The maximum height the child can reach at location 3 can be found using the conservation of energy principle, by equating the initial kinetic energy to the gravitational potential energy at the highest point and solving for the unknown height.
Step-by-step explanation:
To calculate the maximum height the child can reach at location 3, we will use the conservation of energy principle. This principle states that in the absence of nonconservative forces such as friction, the total mechanical energy of the system (kinetic energy plus gravitational potential energy) remains constant. Therefore, we can set the child's initial kinetic energy equal to the gravitational potential energy at the highest point.
The kinetic energy (KE) at location 1 is given by KE = 1/2 * m * v2, where m is the mass and v is the velocity. The gravitational potential energy (GPE) at any height h is GPE = m * g * h, where g is the acceleration due to gravity (approximately 9.8 m/s2).
At location 3, all of the initial kinetic energy will have been converted into gravitational potential energy, so:
- Calculate initial kinetic energy: KE = 1/2 * 49 kg * (7.0 m/s)2
- Set this equal to the potential energy at the top: KE = m * g * h
- Solve for h: h = KE / (m * g) = (1/2 * 49 kg * (7.0 m/s)2) / (49 kg * 9.8 m/s2)
When you calculate h, you'll get the maximum height the child can reach at location 3. Given the options a. 2.5 m b. 3.2 m c. 4.1 m d. 5.7 m, you can calculate to find the correct choice.