Final answer:
The potential energy at the maximum height is 38.90 J. The kinetic energy of the stone on reaching the ground is 37.13 J.
Step-by-step explanation:
(i) To calculate the potential energy at the maximum height, we can use the formula:
Potential Energy (PE) = mass (m) * gravitational acceleration (g) * height (h)
Given that the mass of the stone is 350 g (0.35 kg) and the height it reaches is the maximum height, we need to find the height first. To find the height, we can use the formula:
Final velocity (v) = Initial velocity (u) - gravitational acceleration (g) * time (t)
Since the stone is thrown vertically up, the final velocity at the maximum height is 0 m/s. The initial velocity is 15 m/s and gravitational acceleration is 9.8 m/s^2. We can rearrange the formula to solve for time:
0 = 15 - 9.8 * t
Solving for t, we get t = 1.53 s. Now we can plug this value of t into the formula for height:
Height (h) = Initial velocity (u) * time (t) - 0.5 * gravitational acceleration (g) * time (t)^2
Plugging in the values, we get h = 15 * 1.53 - 0.5 * 9.8 * (1.53)^2 = 11.54 m. Now we can calculate the potential energy:
PE = 0.35 * 9.8 * 11.54 = 38.90 J
(ii) To calculate the kinetic energy of the stone on reaching the ground, we can use the formula:
Kinetic Energy (KE) = 0.5 * mass (m) * velocity (v)^2
At the maximum height, the stone has zero velocity. So, the velocity on reaching the ground will be the same as the initial velocity, which is 15 m/s. Plugging in the values, we get:
KE = 0.5 * 0.35 * 15^2 = 37.13 J
Learn more about Potential and Kinetic Energy