Final answer:
The velocity of a ball thrown up into the air can be determined using the equation v = -9.8t + 10. The initial velocity of the ball is 4.90 m/s, and it takes the ball 2.04 seconds to reach its highest point. The total flight time of the ball is 4.08 seconds, and the maximum height reached by the ball is 9.9 meters.
Step-by-step explanation:
Given that the velocity of the ball after t seconds is given by v = -9.8t + 10, and the mass of the ball is 0.5 kilograms, we can analyze the motion of the ball using the principles of kinematics.
1. To find the initial velocity of the ball, we need to consider the graph of the ball's vertical velocity over time. The graph starts at 4.90 m/s and has a slope of -9.8 m/s². Therefore, the initial velocity of the ball is 4.90 m/s.
2. To determine the time it takes for the ball to reach its highest point, we set the velocity equal to zero and solve for t. Therefore, -9.8t + 10 = 0, which gives us t = 2.04 seconds.
3. The ball will take the same amount of time to fall back down. Therefore, the total time for the ball's flight is 2.04 + 2.04 = 4.08 seconds.
4. To find the maximum height reached by the ball, we can use the kinematic equation s = ut + 0.5at², where s is the displacement, u is the initial velocity, t is the time, and a is the acceleration.
5. Using the equation s = ut + 0.5at² and plugging in the values, we find: s = (4.9)(2.04) + 0.5(-9.8)(2.04)² = 9.9 meters.