Final answer:
To determine when a ball with an initial speed of 245 m/s reaches a height of 19.6m, a quadratic equation derived from the kinematic equations of motion is used.
The ball does not reach a height of 19.6 m when thrown upward with an initial speed of 245 m/s.
Step-by-step explanation:
To solve this problem, we use the kinematic equations of motion.
The initial velocity of the ball is 245 m/s. The acceleration due to gravity is 9.8 m/s^2.
The ball reaches a maximum height when its final velocity becomes 0 m/s.
Using the equation v^2 = u^2 + 2as, where u is the initial velocity, v is the final velocity, a is the acceleration, and s is the distance, we can calculate the maximum height.
In this case, u = 245 m/s, v = 0 m/s, a = -9.8 m/s^2 (negative because the ball is moving upwards), and s is the unknown value.
So, 0^2 = 245^2 + 2(-9.8)s.
Solving for s gives us s = -3000 m.
Since the height cannot be negative, we discard this value.
Therefore, the ball does not reach a height of 19.6 m.