To find the time taken by the stone to reach the maximum height, we can use the equation for vertical motion under constant acceleration. In this case, the stone is thrown vertically upward, and gravity acts as the constant acceleration pulling it downward. Here's how we can calculate the time:
Determine the initial vertical velocity: The stone is thrown vertically upward with an initial velocity of 10 m/s. Since the stone is moving upward, we assign a positive value to the initial velocity: v₀ = 10 m/s.
Determine the acceleration due to gravity: The acceleration due to gravity is acting downward and is typically denoted by the symbol "g." In this case, you mentioned that the acceleration due to gravity is 10 m/s². We assign a negative value to represent the downward direction: a = -10 m/s².
Calculate the time to reach maximum height: At the maximum height, the stone will momentarily come to rest before starting its descent. This means that the final vertical velocity at maximum height (v) will be zero. We can use the following equation of motion to find the time (t): v = v₀ + at.
Plugging in the values: 0 = 10 m/s + (-10 m/s²) * t.
Simplifying the equation: 0 = 10 m/s - 10 m/s² * t.
Rearranging the equation to isolate the time (t): 10 m/s² * t = 10 m/s. t = 10 m/s / 10 m/s².
t = 1 second.
Therefore, the time taken by the stone to reach the maximum height is 1 second.