Final answer:
The ball reached a height of 78.4 meters and was thrown with an initial velocity of -39.2 m/s (upward direction). Therefore, option (B) is correct.
Step-by-step explanation:
To find the height the ball reached and its initial velocity, we can apply the principles of projectile motion. When a ball is thrown up and caught by the thrower, it follows a vertical trajectory. The height it reached can be determined using the formula:
h = ut + (1/2)gt^2
where h is the height, u is the initial velocity, t is the time, and g is the acceleration due to gravity. In this case, the ball is caught after 4 seconds, so we can plug in the values:
h = ut + (1/2)gt^2
h = (0)t + (1/2)(9.8)(4)^2
Simplifying, we get:
h = (1/2)(9.8)(16)
h = 78.4 m
Therefore, the ball reached a height of 78.4 meters.
To find the initial velocity, we can use the equation:
v = u + gt
where v is the final velocity, u is the initial velocity, g is the acceleration due to gravity, and t is the time. In this case, the final velocity is 0 m/s (since the ball is caught), and the time is 4 seconds. Plugging in the values, we get:
0 = u + (9.8)(4)
Solving for u, we get:
u = -9.8(4)
u = -39.2 m/s
Therefore, the ball was thrown with an initial velocity of -39.2 m/s (negative indicates upward direction).