To determine the time it takes for the stone to reach the highest point, we can use the equations of motion under constant acceleration. In this case, we'll assume that the only force acting on the stone is gravity, neglecting air resistance.
The upward motion of the stone will eventually come to a stop at the highest point, where its vertical velocity becomes zero before it starts falling back down. At this point, the stone's final velocity in the upward direction is zero.
The equation we can use to find the time it takes to reach the highest point is:
v_f = v_i + a * t
where: v_f = final velocity (zero in this case) v_i = initial velocity (15 m/s) a = acceleration due to gravity (approximately -9.8 m/s^2, considering it acts in the opposite direction to the upward motion) t = time
Substituting the known values into the equation:
0 = 15 m/s + (-9.8 m/s^2) * t
Simplifying the equation:
9.8 m/s^2 * t = 15 m/s
t = 15 m/s / 9.8 m/s^2
Calculating the value:
t ≈ 1.53 seconds
Therefore, it takes approximately 1.53 seconds for the stone to reach the highest point.