When the ball is thrown straight up in the air, it experiences a constant acceleration due to gravity, which is approximately -9.8 m/s² (assuming negligible air resistance).
To find the velocity of the ball when it comes back down to the person's hand, we can use the fact that the final velocity when the ball reaches its maximum height will be zero. At that point, the ball starts falling back down, and we can use the same acceleration value to calculate its velocity.
Using the equation of motion for velocity:
v = u + at
Where: v is the final velocity u is the initial velocity a is the acceleration t is the time
Let's calculate the time it takes for the ball to reach its maximum height. Since the initial velocity is upward, we can assume the final velocity is zero:
0 = 15 m/s - 9.8 m/s² * t_max
Solving for t_max:
9.8 m/s² * t_max = 15 m/s t_max = 15 m/s / 9.8 m/s² t_max ≈ 1.53 seconds
The total time for the ball's motion is twice the time it takes to reach the maximum height because it spends an equal amount of time going up and coming back down. Therefore, the total time for the ball to return to the person's hand is approximately 2 * t_max ≈ 2 * 1.53 seconds ≈ 3.06 seconds.
Now, we can find the velocity when the ball comes back down by plugging the time and acceleration into the velocity equation:
v = 15 m/s - 9.8 m/s² * 3.06 s v ≈ -14.9 m/s
The velocity is approximately -14.9 m/s when the ball comes back down to the person's hand. The negative sign indicates that the velocity is in the opposite direction of the initial upward velocity.