To determine the maximum height attained by an object thrown straight up with an initial velocity of 80 m/s, we can use the equations of motion for vertical motion under constant acceleration.
The object thrown straight up will experience a constant acceleration due to gravity acting in the opposite direction of its motion. The acceleration due to gravity near the surface of the Earth is approximately 9.8 m/s² (negative because it acts in the opposite direction of motion).
The equation that relates the final velocity (vf), initial velocity (vi), acceleration (a), and displacement (d) is:
vf² = vi² + 2ad
At the maximum height, the final velocity is zero (vf = 0) because the object momentarily stops before falling back down. The initial velocity (vi) is 80 m/s, and the acceleration (a) is -9.8 m/s². We want to find the displacement (d), which represents the maximum height.
Using the equation and rearranging for displacement (d), we have:
0 = (80 m/s)² + 2(-9.8 m/s²)d
Simplifying the equation:
0 = 6400 m²/s² - 19.6 m/s² d
Rearranging for d:
19.6 m/s² d = 6400 m²/s²
d = (6400 m²/s²) / (19.6 m/s²) d ≈ 326.53 meters
Therefore, the maximum height attained by the object is approximately 326.53 meters.