Final answer:
To determine how far off the ground the ball is at the end of 0.5 s, we can use the equation for vertical displacement. The ball will reach the same height twice during its trajectory, so we need to calculate the total time of flight to determine when the ball will be at this height again.
Step-by-step explanation:
To calculate how far off the ground the ball is after 0.5 s, we need to consider its vertical displacement. The ball is thrown straight up, so it will reach its maximum height and then fall back down. The height of the ball at any time can be calculated using the equation: h = h0 + v0t - 0.5gt^2, where h is the height, h0 is the initial height, v0 is the initial velocity, t is the time, and g is the acceleration due to gravity.
Since we are only concerned with the height at 0.5 s, we can plug the values into the equation and calculate the height. The ball's initial height is 0 m since it starts from the ground, the initial velocity is positive because it is thrown upward, and the time is 0.5 s. Substitute these values into the equation to find the height of the ball at 0.5 s.
To find out when the ball will be at this height again, we need to consider that the ball will reach the same height twice during its trajectory, once on its way up and once on its way down. So, the ball will be at this height again when it reaches the ground. To calculate the total time of flight, we can use the equation: t_total = 2 * t_max, where t_total is the total time of flight and t_max is the time it takes for the ball to reach its maximum height.
This information is not provided in the given question, so we need to calculate the time it takes for the ball to reach its maximum height using the equation: v = v0 - gt, where v is the final velocity, v0 is the initial velocity, g is the acceleration due to gravity, and t is the time. The final velocity at the maximum height is 0 m/s because the ball momentarily stops before falling back down. So, we can plug the values into the equation and solve for t_max. Once we have t_max, we can calculate t_total by multiplying it by 2.