The horizontal speed has no effect on the answer.
It doesn't matter whether you flick a marble horizontally from the roof,
fire a high-power rifle horizontally from the roof, drive a school bus straight
off the roof, or drop a bowling ball from the roof with zero horizontal speed.
Their vertical speed is completely determined by gravity, (and it happens to
be the same for all of them).
Handy dandy formula for the distance covered by anything that starts out
with zero speed and accelerates to the end:
Distance = (1/2) (acceleration) x (time)²
If the beginning of the journey is on Earth, then the acceleration is
9.8 m/s² ... the acceleration of gravity on Earth. We'll assume that
the 55-meter rooftop in the question is part of a building on Earth.
55 meters = (1/2) (9.8 m/s²) x (time)²
Divide each side
by 4.9 m/s² : 55 m / 4.9 m/s² = (time)²
(time)² = (55/4.9) sec²
Square-root
each side: time = √(55/4.9 sec²)
= 3.35 sec .
The acceleration due to gravity serves as the centripetal acceleration of the objects that orbits the Earth. The centripetal acceleration due to gravity is calculated through the equation,
a = v²/r
where v is the speed and r is the radius. Substituting the known values to the equation,
9.8 m/s² = (420 m/s)² / r
The value of r from the equation is 18000 m or equal to 18 km.
<em>Answer: 18 km</em>
