The time it takes for a ball thrown vertically upwards to reach its maximum height can be determined using the laws of motion.
When a ball is thrown vertically upwards, its initial velocity is positive, and it decelerates due to the force of gravity until it reaches its maximum height where its velocity becomes zero. At that point, the ball starts descending.
The time it takes for the ball to reach its maximum height can be calculated using the formula for time:
t = v / g
where: t is the time taken, v is the initial vertical velocity, g is the acceleration due to gravity.
In this case, since the ball is thrown vertically upwards, the initial vertical velocity is positive, and the acceleration due to gravity is negative (opposite to the direction of motion).
Therefore, the time taken to reach the maximum height can be calculated by dividing the initial vertical velocity by the acceleration due to gravity.
It's important to note that air resistance is neglected in this calculation, assuming it does not significantly affect the motion of the ball.
So, the time taken for the ball to reach its maximum height can be calculated as follows:
t = |v| / g
where |v| represents the magnitude of the initial vertical velocity.