To determine the time it takes for the stone to reach the highest point, we can use the known initial velocity and the acceleration due to gravity.
When the stone reaches its highest point, its vertical velocity becomes zero before it starts descending. We can use the kinematic equation for vertical motion to find the time it takes to reach this point.
The equation for vertical displacement (y) as a function of time (t) is:
y = v_iy * t + (1/2) * g * t^2
where v_iy is the vertical component of the initial velocity (15 m/s) and g is the acceleration due to gravity (-9.8 m/s²).
At the highest point, the stone reaches its maximum height, so y = 0. Therefore, we can rewrite the equation as:
0 = v_iy * t + (1/2) * g * t^2
Rearranging the equation:
(1/2) * g * t^2 = -v_iy * t
Dividing both sides by t:
(1/2) * g * t = -v_iy
Substituting the values:
(1/2) * (-9.8 m/s²) * t = -(15 m/s)
Simplifying the equation:
-4.9 t = -15
Dividing both sides by -4.9:
t = 15 / 4.9
Calculating the value:
t ≈ 3.06 seconds
Therefore, it takes approximately 3.06 seconds for the stone to reach the highest point.