Answer:
v = 2.928 10³ m / s
Explanation:
For this exercise we use Newton's second law where the force is the gravitational pull force
F = ma
a = F / m
Acceleration is
a = dv / dt
a = dv / dr dr / dt
a = dv / dr v
v dv = a dr
We substitute
v dv = a dr
∫ v dv = 1 / m G m M ∫ 1 / r² dr
We integrate
½ v² = G M (-1 / r)
We evaluate from the lower limit v = 0 for r = R m to the upper limit v = v for r = R + 2.73 10³, where R is the radius of Saturn's moon
v² = 2G M (- 1 / R +2.73 10³+ 1 / R)
We calculate
v² = 2 6,674 10⁻¹¹ 1.10 10²¹ (10⁻³ / 5.61 - 10⁻³ /(5.61 + 2.73))
v² = 14.6828 10⁷ (0.1783 -0.1199)
v = √8.5748 10⁶
v = 2.928 10³ m / s
Answer:
Explanation:
The distance travelled in the free fall is H - h
Since the apple originally started from rest we can use v^2 = u^2 + 2 x g x s where v is the final velocity, g the accln due to gravity and s the distance travelled and u is the initial velocity = 0
So the velocity just before it enters the grass is sq rt [2 x g x (H - h)]
Once in the grass, it slows down at a constant rate which means that the acceleration (a) during this period is constant.
So once again using the same formula we have v = O and u = sq rt[2 x g x (H-h)]
so since v^2 = u^2 + 2 x a x s then
O^2 = 2 x g x (H-h) + 2 x a x h
{O^2 - 2 x g x (H - h)}/(2 x h) = a