What is the factor involved in increasing an object’s inertia?

Slick Willy was traveling at a speed of 61578948 m/s to witness this phenomenon. To arrive at this conclusion, we apply the equation: λ = λ (687 nm) = 570 nm = 61578948 m/s.

Answer:

The BMX rider lands 5.4 meters horizontally away from the ramp's end.

Explanation:

The BMX position vector is represented as:

r = (x0 + v0 × t × cos α, y0 + v0 × t × sin α + ½ × g × t²)

Where:

r = position at time t

x0 = initial horizontal position

v0 = initial speed

α = angle of jump

y0 = initial vertical height

g = gravitational acceleration (-9.8 m/s², upward positive)

Refer to the diagram for clarity. At the landing time, the vertical coordinate of the position vector is -2.4 m, measured from the ramp's edge as the origin. Using the vertical component equation for y, one can solve for t, then substitute t to find the horizontal distance.

The vertical position equation:

-2.4 m = 0 + 5.9 m/s × t × sin 40° - ½ × 9.8 m/s² × t²

Rearranged:

0 = -4.9 t² + 5.9 t × sin 40° + 2.4

Solving this quadratic yields:

t = 1.2 seconds

Then, calculate horizontal distance:

x = 0 + 5.9 m/s × 1.2 s × cos 40° = 5.4 m

This means the BMX lands 5.4 meters from the ramp's edge.

Have a great day!

The alteration in kinetic energy is

Clarification:

According to the work-energy principle, the task performed on an object corresponds to the alteration in its kinetic energy. In mathematical terms:

where:

W signifies the work performed on the object

denotes the kinetic energy at the end

indicates the kinetic energy at the start

Furthermore, when the force is exerted in line with the object’s motion, the work done is expressed as:

Here,

F represents the force’s magnitude

denotes the object’s displacement

In this scenario, the force impacting the object is

F

While the distance moved is the horizontal length traveled, hence

Consequently, the work accomplished is

Thus, the alteration in kinetic energy amounts to

Learn more about work and kinetic energy:

Response:

(b) 10 Wb

Clarification:

Given;

angle of the magnetic field, θ = 30°

initial area of the plane, A₁ = 1 m²

initial magnetic flux through the plane, Φ₁ = 5.0 Wb

The equation for magnetic flux is;

Φ = BACosθ

where;

B denotes the magnetic field strength

A represents the area of the plane

θ is the inclination angle

Φ₁ = BA₁Cosθ

5 = B(1 x cos30)

B = 5/(cos30)

B = 5.7735 T

Next, calculate the magnetic flux through a 2.0 m² section of the same plane:

Φ₂ = BA₂Cosθ

Φ₂ = 5.7735 x 2 x cos30

Φ₂ = 10 Wb

<pHence, the magnetic flux through a 2.0 m² area of the same plane is 10 Wb.

Option "b"

Answer:

θ = 61.3°

Alicia must swim at an angle of 61.3°

Explanation:

Parameters given include:

Width of the river = 100 m

Alicia's speed in still water = 2.5 m/s

Speed of river's current = 1.2 m/s

The angle she needs to swim can be determined by combining the velocities, taking into account the current's influence.

Her swimming speed aimed against the current must offset the current's velocity;

2.5cosθ - 1.2 = 0

2.5cosθ = 1.2

cosθ = 1.2/2.5

θ = cosinverse(1.2/2.5)

θ = 61.3°