<u>Answer</u>
27.7
<u>Explanation</u>
The ball was hit at an angle of 30°, with the horizontal at a speed of 10 m/s. We have to find the horizontal component of speed.
cosx = adjacent/hypotenuse
cos 30 = adjacent / 10
adjacent = 10 cos30
= 8.66 m/s ⇒ This is the horizontal speed.
Now find the horizontal distance.
Distance = speed × time
= 8.66 × 3.2
= 27.71
Answer to the nearest tenth = 27.7
The correct order is (in decreasing order of gravity strength)
Jupiter - Neptune - Venus - Mars
In fact, Wayne's weight on each planet is given by

where m is Wayne's mass, which is a constant value, and g is the gravity strength at the surface of the planet. Therefore, the Wayne's weight W on each planet is directly proportional to the gravity strength of that planet: so the planet with the strongest gravity is the one where Wayne's weight is the greatest (Jupiter, 333 pounds), followed by Neptune (159), Venus (128) and Mars (53).
The resultant vector can be determined by the component vectors. The component vectors are vector lying along the x and y-axes. The equation for the resultant vector, v is:
v = √(vx² + vy²)
v = √[(9.80)² + (-6.40)²]
v = √137 or 11.7 units
The change in electric potential energy of the ion is equal to the charge multiplied by the voltage difference:

where the charge q of the na+ ion is equal to one positive charge, so it's equal to the proton charge:

, and Vf and Vi are the final and initial voltages.
Substituting the numbers, we find:
k = spring constant of the spring = 85 N/m
m = mass of the box sliding towards the spring = 3.5 kg
v = speed of box just before colliding with the spring = ?
x = compression the spring = 6.5 cm = 6.5 cm (1 m /100 cm) = 0.065 m
the kinetic energy of box just before colliding with the spring converts into the spring energy of the spring when it is fully compressed.
Using conservation of energy
Kinetic energy of spring before collision = spring energy of spring after compression
(0.5) m v² = (0.5) k x²
m v² = k x²
inserting the values
(3.5 kg) v² = (85 N/m) (0.065 m)²
v = 0.32 m/s