Final answer:
To determine the maximum height of the object thrown vertically upward, we can use the equation for the final velocity in terms of initial velocity, acceleration, and displacement. Given that the object has a speed of 25 m/s when it reaches two-thirds of its maximum height, we can calculate the maximum height using the given information.
Step-by-step explanation:
To determine the maximum height of the object thrown vertically upward, we can use the equation for the final velocity in terms of initial velocity, acceleration, and displacement:
v^2 = u^2 + 2as
Where v is the final velocity, u is the initial velocity, a is the acceleration (in this case, the acceleration due to gravity, which is -9.8 m/s^2), and s is the displacement.
Given that the object has a speed of 25 m/s when it reaches two-thirds of its maximum height, we can assume that the final velocity is 25 m/s and the initial velocity is 0 m/s (at the highest point, the object momentarily comes to rest before falling back down). We also know that the displacement at two-thirds of the maximum height is two-thirds of the maximum height.
Using these values, we can solve for the maximum height:
25^2 = 0^2 + 2(-9.8)s
s = (25^2)/(2(9.8))
s ≈ 31.89 m
Therefore, the maximum height of the object is approximately 31.89 meters.