Final answer:
The initial velocity of the ball is -5 m/s. The ball takes approximately 0.51 seconds to reach its maximum height. The final velocity of the ball is -5 m/s if it returns to where it was thrown from. The total time the ball is in the air is approximately 1.02 seconds.
Step-by-step explanation:
a) What is the initial velocity of the ball?
To find the initial velocity of the ball, we need to consider the motion of the ball when it reaches its maximum height. At the maximum height, the velocity of the ball is zero since it momentarily stops before falling back down due to gravity. Therefore, the initial velocity of the ball is the same as the final velocity when it was thrown. Since the ball was thrown straight up, the final velocity is negative since it is in the opposite direction of the initial velocity. So, the initial velocity of the ball is -5 m/s.
b) How long does it take for the ball to reach its maximum height?
To find the time it takes for the ball to reach its maximum height, we can use the kinematic equation:
vf = vi + at
At the maximum height, the final velocity is zero and the acceleration is the acceleration due to gravity (-9.8 m/s^2). Plugging these values into the equation, we get:
0 = -5 + (-9.8)t
Solving for t, we find that it takes approximately 0.51 seconds for the ball to reach its maximum height.
c) What is the final velocity of the ball if it returns to where it was thrown from?
Since the final velocity is zero when the ball reaches its maximum height, and the ball returns to where it was thrown from, the final velocity when it reaches back to the starting point is the same as the initial velocity. So, the final velocity is -5 m/s.
d) What is the total time the ball is in the air?
The total time the ball is in the air can be found by doubling the time it takes for the ball to reach its maximum height. So, the total time the ball is in the air is approximately 2 x 0.51 = 1.02 seconds.