A large boulder is ejected vertically upward from a volcano with an initial speed of 41.0 . Air resistance may be ignored.
and the question is?
Thank you. I figure out the answer for this one. I do have another one.
To solve this problem, we need to know the initial speed of the boulder, which is given as 41.0 m/s. We also need to understand that air resistance is ignored in this scenario.
Now, if the boulder is ejected vertically upward, it will eventually reach the highest point of its trajectory and then start falling back down due to the force of gravity. At the highest point of its trajectory, the boulder's vertical velocity will be 0 m/s.
To find the maximum height reached by the boulder, we can use the kinematic equation that relates the final velocity (vf), initial velocity (vi), acceleration (a), and displacement (d):
vf^2 = vi^2 + 2ad
In this case, the final velocity at the highest point is 0 m/s, and the initial velocity is 41.0 m/s. Since the boulder is moving vertically upward, the acceleration due to gravity (a) is -9.8 m/s^2, assuming positive upward and negative downward.
0^2 = (41.0)^2 + 2(-9.8)d
Simplifying the equation:
0 = 1681 - 19.6d
Rearranging the equation to solve for the displacement (d):
19.6d = 1681
d = 1681 / 19.6
Calculating the value:
d = 85.7653 m
Therefore, the maximum height reached by the boulder is approximately 85.77 meters.