An object thrown vertically upward with initial velocity from the surface of the Earth reaches a height H before falling back toward the Earth. If initial velocity is doubled, the object reaches a maximum height equal to ________. Ignore air resistance.

double the height of H

To find the maximum height reached by an object thrown vertically upward, we can use the kinematic equation for vertical motion:

h = (vi^2) / (2g)

where:
h = maximum height
vi = initial velocity
g = acceleration due to gravity

In this case, we are told that the initial velocity is doubled. Let's assume the initial velocity is v, so when it is doubled, it becomes 2v.

When the initial velocity is v, the object reaches a height H. Plugging these values into the equation:

H = (v^2) / (2g)

When the initial velocity is doubled (2v), we want to find the new maximum height, let's call it h2. Plugging values into the equation:

h2 = ((2v)^2) / (2g)
= (4v^2) / (2g)
= 2(v^2) / g

Comparing the two equations, we can see that h2 is twice the height as H. So, the object reaches a maximum height equal to 2H when the initial velocity is doubled.