# A projectile is launched vertically from the surface of the Moon with an initial speed of 1210 m/s. At what altitude is the projectile's speed two-fifths its initial value?

## Oh well, as a first guess since you did not say I will assume g moon = g earth/6

= 9.8/6 = 1.63 m/s^2

so

a = -1.6

v = Vi - 1.6 t

(2/5)(1210) = 1210 - 1.6 t

1.6 t = 1210 (3/5)

t = 454 seconds

h = Vi t - ((1/2)(1.6) t^2

= 384,447 meters

## the mass of the moon is M=7.35e22

and the radius= 1.738 e6

I used the formula

1/2m(2/5vi)^2 - GMm/h+R= 1/2vi^2-GMm/R

Where little m cancels out and solved for h. But my answer and the answer you just gave me was marked wrong.

So you have any other suggestions?

## well, what did you calculate for g moon? If it is not something like 9.81/6 it is wrong, but the 1/6 of earth gravity is a rough approximation.

## 6.67e-11

## Your way I get

(1/2)(21/25) vi^2 = G M [1/R - 1/(R+h) ]

21/50 (1210)^2 = 6.67*10^-11 * 7.35*10^22

[ 1/1.74*10^6 - 1/(1.74*10^6+h) ]

.615*10^6=49*10^11 (.575*10-6 - z)

where

z = 1/(1.74*10^6+h)

.1255*10^-6 = .575*10^-6 - z

z = .449*10^-6

1/z = 2.22*10^6 = 1.74 *10^6 + h

h = .485 *10^6

485,000 meters

check our arithmetics

## using your figures

g moon = F/m = G M/r^2

= 6.67^10^-11*7.35*10^22 /3.03*10*12

=16.17*10^-1 = 1.67 m/s^2

I guessed 9.8/6 = 1.63 so I would be a little off

## okay, I got it thanks !

## Great !

## To find the altitude at which the projectile's speed is two-fifths its initial value, we need to apply the laws of motion, particularly the equations of motion for a vertically launched projectile.

First, let's analyze the given information:

- Initial speed (u) = 1210 m/s

- Final speed (v) = (2/5) * initial speed = (2/5) * 1210 m/s

- Acceleration due to gravity (g) = 1.62 m/s² (on the Moon)

Now, let's use the equations of motion to find the altitude (h) at which the speed is two-fifths its initial value:

1. The equation for the final speed (v) in terms of initial velocity (u), acceleration (g), and height (h) is given by:

v² = u² + 2gh

Rearranging the equation, we can solve for h:

h = (v² - u²) / (2g)

2. Substituting the given values into the equation:

h = [(2/5) * 1210 m/s]² - (1210 m/s)² / (2 * 1.62 m/s²)

Calculating this equation will yield the desired altitude.