How high can a rocket travel if it is initially shot vertically at a velocity of 28.50 ms if the rocket has a mass of 0.500 kg?

Answer 1

The question is describing something more like a cannonball than a rocket.

The mass of a rocket is continually decreasing as the fuel load is burned.

The object in the question has a constant volume, so it might as well be a

bullet or a rock.

Once we notice that, we realize that the question is nothing but a medieval misconception

dressed up in a space-age suit ... the notion that heavy objects run out of oomph sooner

than light ones do when launched vertically, and that the heavier ones then fall back

faster than the lighter ones.

In fact, it makes no difference what the mass of the projectile is. Shot vertically at

a speed of 28.5 meters per second, the speed of a stone or a battleship slows by

9.8 meters per second every second ... the acceleration of gravity. So it continues to

rise for (28.5/9.8) = 2.908 seconds .

The speed at the bottom is 28.5 m/s. The speed at the top is zero.

The average speed before it reaches the top is (28.5/2) = 14.25 m/s.

The distance traveled from the bottom to the top is (14.25) x (2.908) = 41.44 meters .

The purist will object that our result cannot be accurate. because the thing has been

launched vertically, directly away from the center of the earth, and the acceleration

of gravity steadily decreases as our projectile rises. We welcome the purist's objection,

and we shall deal with it in the Appendix.

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Appendix.

The acceleration of gravity decreases with altitude from the earth's surface, so

the accuracy of our conclusion must be tested by sampling the acceleration of

gravity in the first 42 meters above the surface.

The acceleration of gravity is inversely proportional to the projectile's distance

from the center of the earth.

Earth equatorial diameter = 12,756 Km.

Radius = 6,378 km.

Relative gravity at 42 meters' altitude = (6,378 / 6,378.042)2 = 0.9999868 .

Since we only used a single decimal place for the acceleration of gravity altogether,

and had no intention of pursuing anything to to the fifth place, we felt justified in

ignoring a variation in gravity of this magnitude.