problem A newly established colony on the Moon launches a capsule vertically with an initial speed of 1.445 km/s. Ignoring the rotation of the Moon, what is the maximum height reached by the capsule

104.4km

Explanation:

Projectile motion occurs when object is launched into air and allowed to fall freely under the influence of gravity.

Maximum height reached by the object is expressed as;

H = u²sin² (theta) / 2g where;

u is the initial velocity = 1.445km/s

u = 1445m/s since 1000m is equivalent to 1km

theta is the angle of launch

g is the acceleration due to gravity = 10m/s²

theta = 90° (since object is launched vertically)

Substituting the values in the formula we have;

H = 1445² (sin90°) ²/2 (10)

H = 1445²/20

H = 104,401.25m

H = 104.4km

The the maximum height reached by the capsule is 104.4km

Maximum height = 1031km

Explanation:

Given:

Velocity, Vo = 1.445km/s = 1445m/s

Mass of moon = 7.35*10^22kg

Radius of moon = 1737km = 1737000m

Using conservation energy

Ui + Ki = Uf + Kf

--'> (GMm/R) + 1/2 (m ^2)

-GMm / (R + h) - 0

Vo^2 = 2Gm (1/R - 1/R+h)

1445^2 = 2 * (6.67x10^-11) * (7.35*10^22) [ (1/1737000) - (1/1737000 + h) ]

h = 1031km