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## Homework Statement

A missile's trajectory takes it to a maximum altitude of 1200 km.

If its launch speed is 6.2 km/s , how fast is it moving at the peak of its trajectory?

## Homework Equations

K+U = K_o+U_o

U(r) = -GMm/r

## The Attempt at a Solution

Alright some people have been telling me its zero. Intuitively thats what I thought, but

I guess its wrong. Nevertheless, here is my attempt :

K+U = K_o +U_o;

=

1/2mV^2 - GM_eM/r_d = 1/2mV_o^2 - GM_em / r_e

and solving for

V^2 = V_o^2 - 2GM_e/r_e + GM_e/r_d

where,

V_o = 6.2km -> 6.2*1000m

G = universal graity = 6.67*10^-11

M_e = mass of earth = 5.98*10^24

r_e = radius of earth = 6.37 * 10^6;

r_d = distance between the object and the center of earth

= 1200km -> 1200*1000m

and my answer is terms of meters

~2400m

so dividing by 1000

and

v_p ~ 24m/s