# calculus- plz help..

• May 3rd 2006, 01:50 AM
bobby77
calculus- plz help..
The weight (force due to gravity) of an object of mass m and altitude x miles above the surface of the earth is w(x) = (mgR^2)/(R+x)^2, where R is the radius of the earth and g is the acceleration due to gravity. Show that w(x) is approximately mg(1-2x/R). Estimate how large x would need to reduce the weight by 10%.
• May 3rd 2006, 04:22 AM
topsquark
Quote:

Originally Posted by bobby77
The weight (force due to gravity) of an object of mass m and altitude x miles above the surface of the earth is w(x) = (mgR^2)/(R+x)^2, where R is the radius of the earth and g is the acceleration due to gravity. Show that w(x) is approximately mg(1-2x/R). Estimate how large x would need to reduce the weight by 10%.

I solved your first question in another post.

To get an estimate on x, we are looking for an x such that the weight is .9w(0)=.9mg.

$\displaystyle w(x) = .9mg \approx mg \left ( 1- \frac{2x}{R} \right )$

Now solve for x. (This assumes x is small enough to use the above approximation. You should always check that this is true once you get your answer for x.)

-Dan