Physics
posted by Liza .
An object is released from rest at height h above the surface of the Earth, where h is much smaller than the radius of the Earth. It takes t seconds to fall to the ground. At what height should this object be released from rest in order to take 2t seconds to fall to the ground?

Solution: We need to find the connection between the height and time. With “down” positive, so a=g is positive, and with v0 = 0, distance = (1/2) at^2 ? h = (1/2)gt^2 ? h = t^2. Therefore, if we double t, h must increase by a factor of 2^2 = 4.

My Question: I don't understand how they are able to just equate h with t^2 (h=t^2). Then say that the answer is 4h. I thought the answer would be 2gh. But then why is it that gravity isn't included in the final answer?
THANKS!

It is in the final answer, but it has divided out.
h(t)=1/2 g t^2
newheight=1/2 g(2t)^2=1/2 4t^2
so to find newheight, divide the second equation by the first.
hewheight/oldheight=4
newheight=4*oldheight
Respond to this Question
Similar Questions

physics
n object is dropped from rest from a height 5.8 × 106 m above the surface of the earth. If there is no air resistance, what is its speed when it strikes the earth? 
College Algebre
Here is the math problem: The height of an object in free fall, or otherwise thrown into the air near the earth's surface, with initial vertical velocity v0 in feet per seconds, and from the initial height h0 in feet, at any given … 
Physics
a. 2 objects each of mass 200 kg and 500 kg are separated by 50 cm. Where body of mass 20 kg should be placed so that the resultant force of gravity experienced by objects equal to zero? 
physics
If the change in the value of 'g ' at a height 'h ' above the surface of earth is the same as at a depth 'x ' below it. When both x and h are much smaller than the radius of the earth. The relation between x and h is? 
Physics
1.) The earth's radius is about 3956.52 mi. An object that has a mass of 20 kg is taken to a height of 160 km above the earth's surface. a. What is the mass of the object at this height? 
physics
An object is released from rest at an unknown height h above the ground. One second later a second object is released from rest at the same height. When the first object strikes the ground, the second is 20 m above the ground. What … 
Science
An artificial satellite circles around the earth at the height where the gravitational force is one fourth of that at earth's surface. If the earth's radius is R the height of the satellite above the surface of the earth is? 
MATH HELP
A soccer ball is kicked toward the goal. The height of the ball is modeled by the function h(t) = −16t2 + 48t where t equals the time in seconds and h(t) represents the height of the ball at time t seconds. What is the axis of … 
Physics
A 910kg object is released from rest at an altitude of 1200 km above the north pole of the earth. If we ignore atmospheric friction, with what speed does the object strike the surface of the earth? 
algebra
A soccer ball is kicked toward the goal. The height of the ball is modeled by the function h(t) = −16t2 + 48t where t equals the time in seconds and h(t) represents the height of the ball at time t seconds. What is the axis of …