The strength of the gravitational forces between two masses depends on
-- the product of the masses,
-- the distance between their centers of mass.
The time elapsed is 9 seconds
Explanation:
The motion of the ball is a uniformly accelerated motion (a motion with constant acceleration), so we can use the following suvat equation:
where
:
v is the final velocity of the ball
u is the initial velocity
a is the acceleration
t is the time elapsed
For the ball in this problem, we have:
u = 3 m/s is the initial velocity
v = 34.5 m/s is the final velocity
is the acceleration
Solving for t, we find the time taken for this change in velocity:

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By compressing the spring a distance <em>x</em> (in m), you are storing 1/2 <em>k</em> <em>x</em> ² (in J) of potential energy, which is converted completely into kinetic energy 1/2 <em>m v</em> ², where
• <em>k</em> = 40 N/m = spring constant
• <em>m</em> = 10 kg = mass of the ball
• <em>v</em> = 2 m/s = ball's speed (at the moment the spring returns to its equilibrium point)
So we have
1/2 <em>k</em> <em>x</em> ² = 1/2 <em>m</em> <em>v</em> ²
<em>x</em> = √(<em>m</em>/<em>k</em> <em>v</em> ²) = √((10 kg) / (40 N/m) (2 m/s)²) = 1 m