How High Can a Projectile Go When Launched at 10 km/s?

[alexwaylo2008]

Gravitational potential energy. Please help!

Homework Statement

A projectile is launched from Earth's surface at a speed of 10 km/s. Find the maximum height it reaches.

Homework Equations

change in U = -change in K
U = -GM/r

The Attempt at a Solution

GMm/r = 1/2mv^2
((6.67x10^-11)(5.98x10^24))/r = 1/2 (10^4m/s)^2
r = 1.5x10^6 m
the answer is supposed to be 2.5x10^7 m ?

 

[Dick]

Are you really taking a potential energy difference? I.e. GMm/(r-r_E) where r_E is the radius of the earth? Or did you post the wrong exponent? I definitely get 7 for the exponent, but I don't get 2.5*10^7.

 

[ogb p]

I would like to clarify that the given problem does not provide enough information to accurately solve for the maximum height. We need to know the angle at which the projectile is launched and the mass of the projectile. Additionally, the formula used (U = -GMm/r) is for the gravitational potential energy between two objects, not for calculating the maximum height of a projectile. To solve for the maximum height, we would need to use the kinematic equations and take into account the acceleration due to gravity. I suggest reviewing the problem and providing more information to accurately solve it.