Answer:
0.37 m
Explanation:
The angular frequency, ω, of a loaded spring is related to the period, T, by
![\omega = \dfrac{2\pi}{T}](https://tex.z-dn.net/?f=%5Comega%20%3D%20%5Cdfrac%7B2%5Cpi%7D%7BT%7D)
The maximum velocity of the oscillation occurs at the equilibrium point and is given by
![v = \omega A](https://tex.z-dn.net/?f=v%20%3D%20%5Comega%20A)
A is the amplitude or maximum displacement from the equilibrium.
![v = \dfrac{2\pi A}{T}](https://tex.z-dn.net/?f=v%20%3D%20%5Cdfrac%7B2%5Cpi%20A%7D%7BT%7D)
From the the question, T = 0.58 and A = 25 cm = 0.25 m. Taking π as 3.142,
![v = \dfrac{2\times3.142\times0.25\text{ m}}{0.58\text{ s}} = 2.71 \text{ m/s}](https://tex.z-dn.net/?f=v%20%3D%20%5Cdfrac%7B2%5Ctimes3.142%5Ctimes0.25%5Ctext%7B%20m%7D%7D%7B0.58%5Ctext%7B%20s%7D%7D%20%3D%202.71%20%5Ctext%7B%20m%2Fs%7D)
To determine the height we reached, we consider the beginning of the vertical motion as the equilibrium point with velocity, v. Since it is against gravity, acceleration of gravity is negative. At maximum height, the final velocity is 0 m/s. We use the equation
![v_f^2 = v_i^2+2ah](https://tex.z-dn.net/?f=v_f%5E2%20%3D%20v_i%5E2%2B2ah)
is the final velocity,
is the initial velocity (same as v above), a is acceleration of gravity and h is the height.
![h = \dfrac{v_f^2 - v_i^2}{2a}](https://tex.z-dn.net/?f=h%20%3D%20%5Cdfrac%7Bv_f%5E2%20-%20v_i%5E2%7D%7B2a%7D)
![h = \dfrac{0^2 - 2.71^2}{2\times-9.81} = 0.37 \text{ m}](https://tex.z-dn.net/?f=h%20%3D%20%5Cdfrac%7B0%5E2%20-%202.71%5E2%7D%7B2%5Ctimes-9.81%7D%20%3D%200.37%20%5Ctext%7B%20m%7D)
Answer:
103.5 meters
Explanation:
Given that a stunt person has to jump from a bridge and land on a boat in the water 22.5 m below. The boat is cruising at a constant velocity of 48.3 m/s towards the bridge. The stunt person will jump up at 6.45 m/s as they leave the bridge.
The time the person will jump to a certain spot under the bridge can be calculated by using the formula below:
h = Ut + 1/2gt^2
since the person will fall under gravity, g = 9.8 m/s^2
Also, let assume that the person jump from rest, then, U = 0
Substitute h, U and g into the formula above
22.5 = 1/2 * 9.8 * t^2
22.5 = 4.9t^2
22.5 = 4.9t^2
t^2 = 22.5/4.9
t^2 = 4.59
t = ![\sqrt{4.592}](https://tex.z-dn.net/?f=%5Csqrt%7B4.592%7D)
t = 2.143 seconds
From definition of speed,
speed = distance /time
Given that the boat is cruising at a constant velocity of 48.3 m/s towards the bridge, substitute the speed and the time to get the distance.
48.3 = distance / 2.143
distance = 48.3 * 2.143
distance = 103.5 m
Therefore, the boat should be 103.5m away from the bridge at the moment the stunt person jumps?
Answer:
Yes the student is correct
Explanation:
The first law of thermodynamics states that energy can neither be created nor destroyed
The second law of thermodynamics states that the entropy (disorderliness) of an isolated system always increases
Therefore, whereby energy is not supplied to maintain the orderly oscillatory motion with constant amplitude, the amplitude of the system is bound to reduce with time that is the vibration of the system must be damped
Answer:
5.1 kg
Explanation:
Its mass on the moon is 5.1 kg because mass is an intrinsic property of a material and does not change with location. Although, its weight might vary because its acceleration of gravity g is dependent on the mass M and radius r of the planet(in this case, moon) involved g = GM/r². Since weight W = mg is dependent o g, weight varies but mass remains constant.
Hi there!
I believe the answer is transversal or transverse.