Answer:
The spring's maximum compression will be 2.0 cm
Explanation:
There are two energies in this problem, kinetic energy 
and elastic potential energy 
(with m the mass, v the velocity, x the compression and k the spring constant. ) so the total mechanical energy at every moment is the sum of the two energies:
Here we have a situation where the total mechanical energy of the system is conserved because there are no dissipative forces (there's no friction), so:
Note that at the initial moment where the hockey puck has not compressed the spring all the energy of the system is kinetic energy, but for a momentary stop all the energy of the system is potential elastic energy, so we have:
(1)
Due conservation of energy the equality (1) has to be maintained, so if we let k and m constant x has to increase the same as v to maintain the equality. Therefore, if we increase velocity to 2v we have to increase compression to 2x to conserve the equality. This is 2(1.0) = 2.0 cm
Answer:
Resultant displacement = 38.58 miles at an angle of 23.57° north of west.
Explanation:
Let north represent positive y direction and east represent positive x direction. Unit vector along x direction is represented by i and vector along unit vector along y direction is represented by j
Initial displacement = 17 miles north = 17 j miles
Final displacement = 24 miles at an angle of 40° west of north = 24 miles at an angle of 130° to positive x -axis
= (24 cos 130 i + 24 sin 130 j )
= (-15.43 i + 18.36 j ) miles
Total displacement = 17 j + (-15.43 i + 18.36 j) = -15.43 i + 35.36 j
Magnitude of displacement 
Angle to positive x -axis = tan⁻¹(35.36/-15.43) = 113.57°
Resultant displacement = 38.58 miles at an angle of 23.57° west of north.
Answer:
The velocity of the acorn just before it reaches the ground is 19 m/s
The kinetic energy when hitting the ground is 3.1 J
Explanation:
Given;
mass of the acorn, m = 0.017 kg
height of fall, h = 18.5 m
Apply the law of conservation of mechanical energy;
mgh = ¹/₂mv²
gh = ¹/₂v²
v² = 2gh
v = √2gh
v = √(2 x 9.8 x 18.5)
v = 19 m/s
Thus, the velocity of the acorn just before it reaches the ground is 19 m/s
Now, determine the kinetic energy when hitting the ground;
K.E = ¹/₂mv²
K.E = ¹/₂(0.017)(19)²
K.E = 3.09 J
K.E = 3.1 J
Therefore, the kinetic energy when hitting the ground is 3.1 J
B would be the correct answer
