Final answer:
To find the time it takes for the ball to hit the ground, use the equation t = sqrt(2d/g), where d is the height of the building and g is the acceleration due to gravity. For this question, the time is approximately 3.19 seconds. The ball's velocity just before hitting the ground can be found using 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 taken.
Step-by-step explanation:
To find the time it takes for the ball to hit the ground, we can use the kinematic equation: d = 1/2 * g * t^2, where d is the height of the building, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time taken. Rearranging the equation, we get: t = sqrt(2d/g).
In this case, the height of the building is 50 m, so we substitute that value into our equation: t = sqrt(2 * 50 / 9.8). Solving for t, we get approximately 3.19 seconds.
The ball's velocity just before hitting the ground can be found using the equation: v = u + gt, where v is the final velocity, u is the initial velocity, g is the acceleration due to gravity (-9.8 m/s^2), and t is the time taken. Since the ball is thrown upwards, the initial velocity would be -30 m/s (negative to indicate the direction). Substituting the values, we get: v = -30 + (-9.8) * 3.19. Solving for v, we get approximately -62.56 m/s.