Final answer:
The time it takes for a ball thrown straight up with an initial speed of 5.0 m/s to reach its maximum height is approximately 0.51 seconds when ignoring air resistance.
Step-by-step explanation:
To calculate the time it takes for a ball thrown straight up with an initial speed of 5.0 m/s to reach its maximum height, we use the kinematic equation for uniformly accelerated motion: v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
At the maximum height, the final velocity of the ball is 0 m/s. The acceleration due to gravity is -9.8 m/s2 (negative because it's directed downwards). Plugging in these values:
0 = 5.0 m/s + (-9.8 m/s2)t
t = 5.0 m/s / 9.8 m/s2
t = 0.51 seconds
So, it takes approximately 0.51 seconds for the ball to reach its maximum height, ignoring air resistance.