Answer:
The horizontal range of the projectile = 26.63 meters
Explanation:
Step 1: Data given
Distance above the planet's surface = 630 km = 630000
The ship's orbal speed = 4900 m/s
Radius of the planet = 4.48 *10^6 m
Initial speed of the projectile = 13.6 m/s
Angle = 30.8 °
Step 2: Calculate g
g= GM /R² = (v²*(R+h)) /(R²)
⇒ with v= the ship's orbal speed = 4900 m/S
⇒ with R = the radius of the planet = 4.48 *10^6 m
⇒ with h = the distance above the planet's surface = 630000 meter
g = (4900² * ( 4.48*10^6+ 630000)) / ((4.48*10^6)²)
g = 6.11 m/s²
<u>Step 3:</u> Describe the position of the projectile
Horizontal component: x(t) = v0*t *cos∅
Vertical component: y(t) = v0*t *sin∅ -1/2 gt² ( will be reduced to 0 in time )
⇒ with ∅ = 30.8 °
⇒ with v0 = 13.6 m/s
⇒ with t= v(sin∅)/g = 1.14 s
Horizontal range d = v0²/g *2sin∅cos∅ = v0²/g * sin2∅
Horizontal range d =(13.6²)/6.11 * sin(2*30.8)
Horizontal range d =26.63 m
The horizontal range of the projectile = 26.63 meters
