Answer:
12 units
Explanation:
This problem can be solved if we take into account the equation for a sphere
where we took that the radius is 13 units. If we take z=5 and we replace this value in the equation of the sphere we have
where we have taken x2 +y2 because if the equation of a circunference.
In this case the intersection is made when we take z=5, for this value the sphere and the plane coincides in values.
Hence, the radius is 12 units
I hope this is useful for you
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A) 19.6 m/s (downward)
B) 576 J
C) 19.6 m
D) Velocity: not affected, kinetic energy: doubles, distance: not affected
Explanation:
A)
An object in free fall is acted upon one force only, which is the force of gravity.
Therefore, the motion of an object in free fall is a uniformly accelerated motion (constant acceleration). Therefore, we can find its velocity by applying the following suvat equation:
where:
v is the velocity at time t
u is the initial velocity
is the acceleration due to gravity
For the object in this problem, taking downward as positive direction, we have:
(the object starts from rest)
Therefore, the velocity after
t = 2 s
is:
(downward)
B)
The kinetic energy of an object is the energy possessed by the object due to its motion.
It can be calculated using the equation:
where
m is the mass of the object
v is the speed of the object
For the object in the problem, at t = 2 s, we have:
m = 3 kg (mass of the object)
v = 19.6 m/s (speed of the object)
Therefore, its kinetic energy is:
C)
In order to find how far the object has fallen, we can use another suvat equation for uniformly accelerated motion:
where
s is the distance covered
u is the initial velocity
t is the time
a is the acceleration
For the object in free fall in this problem, we have:
u = 0 (it starts from rest)
(acceleration of gravity)
t = 2 s (time)
Therefore, the distance covered is
D)
Here the mass of the object has been doubled, so now it is
M = 6 kg
For part A) (final velocity of the object), we notice that the equation that we use to find the velocity does not depend at all on the mass of the object. This means that the value of the final velocity is not affected.
For part B) (kinetic energy), we notice that the kinetic energy depends on the mass, so in this case this value has changed.
The new kinetic energy is
where
M = 6 kg is the new mass
v = 19.6 m/s is the speed
Substituting,
And we see that this value is twice the value calculated in part A: so, the kinetic energy has doubled.
Finally, for part c) (distance covered), we see that its equation does not depend on the mass, therefore this value is not affected.