To solve this problem, we need to analyze the motion of the body and determine the time it takes to reach its maximum height, as well as the distance traveled during the 7th and 8th seconds.
When a body is thrown vertically upwards, its initial velocity (u) is 2 m/s, and we can assume the acceleration due to gravity (g) is approximately 9.8 m/s^2.
First, let's calculate the time it takes for the body to reach its maximum height. We can use the following equation:
v = u - g * t
where:
- v is the final velocity (0 m/s at the highest point),
- u is the initial velocity (2 m/s),
- g is the acceleration due to gravity (9.8 m/s^2),
- t is the time taken.
Setting v to 0, we can solve for t:
0 = 2 m/s - 9.8 m/s^2 * t
Solving for t:
t = 2 m/s / 9.8 m/s^2 ≈ 0.204 seconds
Therefore, it takes approximately 0.204 seconds for the body to reach its maximum height.
Next, let's calculate the distance traveled during the 7th second. We know that during the upward motion, the body reaches its maximum height and starts descending. Therefore, the distance traveled during the 7th second can be calculated as the difference between the total distance traveled in the first 7 seconds and the total distance traveled in the first 6 seconds.
The total distance traveled in the first 7 seconds is given by:
distance_7s = u * t + (1/2) * (-g) * t^2
Substituting the values:
distance_7s = 2 m/s * 7 s + (1/2) * (-9.8 m/s^2) * (7 s)^2
distance_7s ≈ 9.8 meters
Now, let's calculate the distance traveled during the 8th second. Since the distance traveled in the 7th and 8th seconds is equal, the distance traveled in the 8th second will also be approximately 9.8 meters.
Finally, let's determine the displacement in the 8th second. Displacement is a vector quantity that takes into account both magnitude and direction. In this case, since the body is thrown vertically upwards, the displacement in the 8th second will be negative, indicating a downward direction.
Therefore, the displacement in the 8th second is approximately -9.8 meters.