A gold puck has a mass of 12 kg and a velocity of 5i – 4j m/s prior to a collision with a stationary blue puck whose mass is 18

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!

Answer:

The force magnitude is  

and it is directed at 57.98° from the horizontal in a counterclockwise manner.

Explanation:

The problem states that

At t = 0,

The angular rate of increase is

Converting to revolutions per second gives us  

The rope length is defined by

                         

    At , Tension T of the rope is 18 kN.

     The weight of the para-sailor is

In analyzing the question, we observe that the equation for length can be represented as a linear displacement equation.

 The derivative of displacement results in velocity.

Hence,

           

signifies the velocity, and further differentiation yields acceleration.

Therefore,

         

Now considering the moment when the rope forms a 30° angle with the water,

typically angular velocity is expressed as

                     

where represents the angular displacement.

Next, evaluating the interval from gives us

                 

making t the focal point.

             

               

At this time, the displacement measures

               

               

The linear velocity computes to

             

               

Whereas linear acceleration calculates as

         

             

Generally, radial acceleration is given by

         

             

             

Simultaneously, angular acceleration can be represented as

                 

Then

Thus,

             

                   

The resultant acceleration is mathematically denoted as

               

                 

                 

Now the acceleration's direction is mathematically expressed as

                 

                       

                           

               

The y-axis force acting on the para-sailor is mathematically shown as

               

                   

                   

The x-axis force acting on the para-sailor is represented as

                 

             

             

The overall force is calculated as

                     

                             

                           

The directional force is evaluated as

             

                   

                       

                       

     

                     

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:

~Greetings! ^_^

Your inquiry: A plant produces flowers with a violet hue. The flowers possess a violet appearance due to their ability to absorb all light waves barring____ rays.

Your reply: A plant produces flowers with a violet hue. The flowers possess a violet appearance because they absorb all light rays except for violet rays.


Hope this is beneficial~

Answer:

Explanation:

When calculating Hall voltage, it is crucial to have the current, magnetic field strength, length, area, and number of charge carriers available. The Hall voltage can be expressed using the equation:

Where:

i= the current

B= the magnetic field strength

L = the length

n = the number of charge carriers

e= charge of an electron

We need to replace values and solve for n:

As a result, the charge carrier density is