The calculated magnitude of the hiker's displacement is , and the direction of this displacement is
.
Further explanation:
Displacement refers to the minimal distance covered by an object from its starting point to its end location.
Given:
The distance traveled by the hiker towards the west is .
The distance covered by the hiker towards the north is .
Concept used:
The hiker begins at point A, moves westward to point B, then travels 100 m north to reach point C. To find the shortest path, we determine the displacement which is from point C back to point A. The path taken by the hiker can be visualized as a right triangle, labeled ABC, with AB as the base, BC as the height, and CA as the hypotenuse.
In accordance with the Pythagorean theorem, “the square of the hypotenuse is equal to the sum of the squares of the other two sides.”
The Pythagorean theorem can be expressed as:
To find the hypotenuse, rearrange the formula:
…… (1)
The angle between side AB and AC can be defined as:
…… (2)
Substituting for AB and
for BC in equation (1) gives:
Similarly, substitute for BC and
for AC in equation (2):
The final result shows that the hiker's shortest distance is in the
at an angle of
.
Learn more:
1. Conservation of momentum
2. Motion under friction
3. Motion under gravitation
Answer Details:
Grade: High School
Subject: Physics
Chapter: Speed and distance
Keywords:
Speed, distance, displacement, velocity, time, magnitude, direction, north, east, west, south, Pythagorean theorem, triangle, sine, cosine, tangent, 224 m, 223.6 m, 26.51 deg, 27 deg.
Answer:
The energy unit is expressed as kg-m/s or Joules.
Explanation:
The relationship between mass and energy in physics is represented by:
Where
m denotes the mass of the object
c signifies the speed of light
In the SI system, mass is measured in kilograms and the speed of light in m/s. Therefore, energy is defined in kg-m/s, which is equal to Joules.
Thus, the appropriate SI unit for energy is kg-m/s or Joules. This concludes the explanation.
Answer:
d_total = 12 m
Explanation:
In this kinematics scenario illustrated in the graph provided, we determine the distance traveled over a 24-second duration.
The comprehensive distance can be calculated as follows:
d_total = d₁ + d₂ + d₃
Given that d₂ on the graph is level (v=0), its distance equates to zero, hence d₂ = 0.
The distance for d₁ is calculated as:
d₁ = 12 - 6 = 6 m
For distance d₃:
d₃ = 6 - 0 = 6 m
Thus, the overall distance covered is:
d_total = 6 + 0 + 6
d_total = 12 m
Answer:
When ice is subjected to heat, it melts; however, the temperature remains constant at 0◦ C.
Explanation:
Solution
The heat supplied by the heater is solely utilized for the melting of the ice, thus maintaining the temperature at 0◦ C.
Once all the ice has liquefied, the temperature of the resulting water will start to rise over time.
Note: please see the attached document with solutions featuring diagrams related to this explanation
Response:
(a) 104 N
(b) 52 N
Clarification:
Provided Information
Incline angle of the ramp: 20°
F forms a 30° angle with the ramp
The parallel component of F along the ramp is Fx = 90 N.
The perpendicular component of F is Fy.
(a)
Consider the +x direction pointing up the slope, and the +y direction perpendicular to the ramp's surface.
Using the Pythagorean theorem, decompose F into its x-component:
Fx=Fcos30°
To find F:
F= Fx/cos30°
Insert the value for Fx based on the given info:
Fx=90 N/cos30°
=104 N
(b) Calculate the y-component of r using the Pythagorean theorem:
Fy = Fsin 30°
Substituting for F from part (a):
Fy = (104 N) (sin 30°)
= 52 N
