Final answer:
To find the initial velocity of a ball thrown upward to reach a height of 3 meters, you use the kinematic equation for vertical motion and solve for the initial velocity, which is approximately 7.67 m/s.
Step-by-step explanation:
To determine the initial velocity of the ball that reaches a height of 3 meters before falling down, we can use the kinematic equations for falling objects. We will apply the equation that relates displacement (s), initial velocity (v0), acceleration (a), and the final velocity (v), which is v2 = v02 + 2as. Since the ball reaches its highest point when it momentarily stops before falling back down, its final velocity at that point is 0 m/s. The acceleration is due to gravity, which is -9.8 m/s2. With a known height (displacement) of 3 m, we can solve for the initial velocity v0.
Substituting our known values into the equation:
0 = v02 - 2(9.8 m/s2)(3 m). From here, we solve for the initial velocity:
v02 = 2(9.8 m/s2)(3 m) = 58.8 m2/s2
v0 = sqrt(58.8 m2/s2) = 7.67 m/s
Therefore, the initial velocity of the ball is approximately 7.67 m/s.