Answer:
141 m at 65.6° N of E
Explanation:
Let E be along the positive x axis of a unit circle
N = 90°
E = 0°
SE = -45°
W = 180°
NW = 135°
east displacement
x = 140cos90 + 85cos0 + 35cos-45 + 38cos180 + 19cos135 = 58.313708... m
north displacement
y = 140sin90 + 85sin0 + 35sin-45 + 38sin180 + 19sin135 = 128.6862915... m
d = √(128.6862915² + 58.313708²) = 141.28216525... m
tanθ = 128.6862915 / 58.313708
θ = 65.622521...
Using kinematic equation s=ut + 1/2 at^2(u = initial velocity=0, s=120m, t= 6.32s), 120 = 0(t) + 1/2 a(6.32)^2. a = 120x2/(6.32)^2 = 6m/s^2.
Answer:
<em>Amplitude= 8 m</em>
Explanation:
<u>The Amplitude of a Wave</u>
Sinusoidal Function refers to a mathematical curve with a smooth and periodic oscillation. Its name comes from the sine function and is characterized by the amplitude or the maximum displacement or distance moved by a point on a vibrating body measured from its equilibrium position.
To calculate the amplitude from a graph, we measure the maximum point and the minimum point the wave reaches. Then we subtract both values and divide the result by 2.
The shown wave in the figure has a maximum value of 8 m and a minimum value of -8 m. The distance from the maximum to the minimum is 8-(-8)= 16 m, thus the amplitude is 16/2= 8m.
Amplitude= 8 m
Answer:
c. Kinetic energy
Explanation:
The two types of energy involved in this problem are:
- Potential energy: it is the energy possessed by an object due to its position. It is calculated as
where
m is the mass of the object
g is the acceleration due to gravity
h is the height of the object relative to the ground
From the formula, we see that the higher the object is above the ground (higher h), the larger the potential energy of the object. In this problem, the pig is falling down, so the value of h is decreasing, therefore the potential energy is decreasing as well.
- Kinetic energy: it is the energy possessed by an object due to its motion. It is given by:
where
m is the mass of the object
v is its speed
In this problem, as the pig falls down, it accelerates, so its speed increases: since the kinetic energy is proportional to the square of the speed, as the speed increases, its kinetic energy increases too. So, the correct answer is
c. Kinetic energy
Explanation:
The forces acting on a massless object (spring, hook, string or wire, if considered massless) will always balance. Balanced forces acting on an object cause it to compress or stretch. The forces acting on a mass will never cancel.
