Final answer:
To find the time it took for the stone to reach its maximum height, we use the equation v = u + at with the initial velocity of 12 m/s and the acceleration due to gravity as 9.81 m/s^2. Hence, the stone takes approximately 1.22 seconds to reach its maximum height.
Step-by-step explanation:
When a stone is projected vertically upwards, it initially moves against the force of gravity. As it rises, its velocity decreases until it reaches its highest point, when its velocity becomes zero. At this highest point, the stone stops momentarily before it starts to fall back downwards.
To calculate the time it takes for the stone to reach its maximum height, we can use the fact that the vertical velocity at the highest point is zero. We can apply the formula for velocity to solve for time:
v = u + at
Where:
v is the final velocity (0 in this case)
u is the initial velocity (12 m/s upwards in this case)
a is the acceleration due to gravity (-9.8 m/s² downwards)
t is the time taken
Rearranging the formula, we get:
t = (v - u) / a
Substituting the values, we have:
t = (0 - 12) / -9.8
t = 12 / 9.8
t ≈ 1.22 seconds