Final answer:
To find the initial velocity and distance of the stone above the ground, use the equation v = vo + at and s = ut + (1/2)at² respectively. To find the velocity and distance at any given time, use the same equations. The velocity at which the stone strikes the ground is 0 m/s.
Step-by-step explanation:
To find the initial velocity of the stone, we can use the equation v = vo + at, where v is the final velocity, vo is the initial velocity, a is the acceleration, and t is the time. In this case, the final velocity is 0 m/s (since the stone is dropped) and the acceleration is the acceleration due to gravity, which is 9.8 m/s². Therefore, vo = 0 + 9.8 × 0 = 0 m/s.
To find the distance traveled by the stone above the ground, we can use the equation s = ut + (1/2)at², where s is the distance, u is the initial velocity, t is the time, and a is the acceleration. In this case, the initial velocity is 0 m/s (as calculated above), the time is the time since the stone was dropped, and the acceleration is the acceleration due to gravity, which is 9.8 m/s². Therefore, s = 0 × t + (1/2) × 9.8 × t² = (4.9 × t²) meters.
To find the velocity of the stone at any given time t, we can use the equation v = vo + at, where v is the final velocity, vo is the initial velocity, a is the acceleration, and t is the time. In this case, the initial velocity vo is 0 m/s, the acceleration a is the acceleration due to gravity, which is 9.8 m/s², and the time t is the time since the stone was dropped. Therefore, v = 0 + 9.8 × t = (9.8 × t) m/s.
Finally, to find the distance of the stone above the ground at any given time t, we can use the equation s = ut + (1/2)at², where s is the distance, u is the initial velocity, t is the time, and a is the acceleration. In this case, the initial velocity u is 0 m/s, the time t is the time since the stone was dropped, and the acceleration a is the acceleration due to gravity, which is 9.8 m/s². Therefore, s = 0 × t + (1/2) × 9.8 × t² = (4.9 × t²) meters.
Finally, to find the velocity of the stone when it strikes the ground, we can use the equation v = vo + at, where v is the final velocity, vo is the initial velocity, a is the acceleration, and t is the time. In this case, the initial velocity vo is 0 m/s, the acceleration a is the acceleration due to gravity, which is 9.8 m/s², and the time t is the time it takes for the stone to fall from the observation deck to the ground. Since we don't have the value for t in this question, we can't calculate the velocity. However, we know that when the stone strikes the ground, its final velocity will be equal to the initial velocity multiplied by -1. Therefore, the velocity with which the stone strikes the ground is 0 m/s × -1 = 0 m/s.