Final answer:
To find the maximum height reached by a stone thrown vertically upward, calculate the time taken to reach the highest point and use it to determine the distance traveled. In this specific problem, with an initial velocity of 21.0 m/s, the maximum height can be found using the equations of motion.
Step-by-step explanation:
The maximum height reached by the stone can be determined using the equations of motion. When a stone is thrown vertically upward, its initial velocity is positive and the acceleration due to gravity is negative. The maximum height is reached when the stone comes to a stop before starting to fall back down.
- First, find the time taken for the stone to reach its highest point using the equation:
- time = final velocity / acceleration
- Next, calculate the distance traveled by the stone during this time using the equation:
- distance = initial velocity * time + 0.5 * acceleration * time^2
- The maximum height reached by the stone is equal to the distance calculated in step 2.
For this specific problem, the stone's initial velocity is 21.0 m/s. The acceleration due to gravity is approximately -9.8 m/s^2. Plugging these values into the equations, we can find the maximum height.