Final answer:
The stone takes approximately 4.08 seconds to reach the ground and has a final speed of approximately -19.9 m/s just before hitting the ground.
Step-by-step explanation:
To solve this problem, we can break it down into two parts: finding the time it takes for the stone to reach the ground and finding the speed just before it hits the ground.
First, let's find the time. We can use the kinematic equation:
vertical distance = initial vertical velocity * time - (1/2) * acceleration * time^2
Given that the stone is thrown upward at an angle of 30 degrees with a speed of 20 m/s and the height of the building is 45 meters, we can determine the initial vertical velocity by:
initial vertical velocity = initial speed * sin(angle)
Then, we can solve for time by rearranging the equation to:
time = (initial vertical velocity + sqrt(initial vertical velocity^2 + 2 * acceleration * vertical distance)) / acceleration
After substituting the values, we get:
time = (20 m/s * sin(30 degrees) + sqrt((20 m/s * sin(30 degrees))^2 + 2 * (-9.8 m/s^2) * 45 m)) / -9.8 m/s^2
By calculating this expression, we find that the time is approximately 4.08 seconds.
Now let's find the speed just before the stone hits the ground. We can use the kinematic equation:
final velocity = initial velocity + acceleration * time
Given that the initial velocity is 20 m/s and the time is 4.08 seconds, we can substitute these values and calculate:
final velocity = 20 m/s + (-9.8 m/s^2) * 4.08 s
This simplifies to:
final velocity = 20 m/s - 39.9 m/s
Therefore, the final velocity just before the stone hits the ground is approximately -19.9 m/s.