Answer: 17.68 s
Explanation:
This problem is a good example of Vertical motion, where the main equation for this situation is:
(1)
Where:
is the height of the ball when it hits the ground
is the initial height of the ball
is the initial velocity of the ball
is the time when the ball strikes the ground
is the acceleration due to gravity
Having this clear, let's find from (1):
(2)
Rewritting (2):
(3)
This is a quadratic equation (also called equation of the second degree) of the form 
, which can be solved with the following formula:
(4)
Where:
Substituting the known values:
(5)
Solving (5) we find the positive result is:
continents, paleoclimate indicators, truncated geologic features, and fossils:D
Answer:
8 mph
Explanation:
4 miles in half hour so you add 4 more for the second half
Answer:
0.3 m
Explanation:
Initially, the package has both gravitational potential energy and kinetic energy. The spring has elastic energy. After the package is brought to rest, all the energy is stored in the spring.
Initial energy = final energy
mgh + ½ mv² + ½ kx₁² = ½ kx₂²
Given:
m = 50 kg
g = 9.8 m/s²
h = 8 sin 20º m
v = 2 m/s
k = 30000 N/m
x₁ = 0.05 m
(50)(9.8)(8 sin 20) + ½ (50)(2)² + ½ (30000)(0.05)² = ½ (30000)x₂²
x₂ ≈ 0.314 m
So the spring is compressed 0.314 m from it's natural length. However, we're asked to find the additional deformation from the original 50mm.
x₂ − x₁
0.314 m − 0.05 m
0.264 m
Rounding to 1 sig-fig, the spring is compressed an additional 0.3 meters.
