When a pendulum is pulled back from its equilibrium position by 10∘, the restoring force is 1.0 N. When it is pulled back to 30∘

Thrust is quantified as a reaction force, in accordance with Newton's third law. When a system accelerates or expels mass in one direction, this resulting mass generates a force of equal strength but in the opposite direction on that system. This relationship can be expressed mathematically as:

Where:

v = velocity of the exhaust gases as perceived from the rocket.

= Change in mass over time

The provided data is as follows:

After substitution, we obtain:

The volumes are 200cm3 and 0.0002m3

Answer:

The resulting velocity for him will be 0.187 m/s in reverse direction.

Explanation:

Given:

The mass of the man is,

The mass of the ball is,

The initial velocity of the man is,

The initial velocity of the ball is,

The final velocity of the ball is,

The final velocity of the man is,

To determine this scenario, we employ the principle of momentum conservation.

This principle states that the total initial momentum equals the total final momentum.

Momentum is calculated by multiplying mass by velocity.

Initial momentum = Initial momentum of the man and the ball

Initial momentum =

Final momentum = Final momentum of the man and the ball

Final momentum =

Hence, the total initial momentum equals the total final momentum

The negative sign indicates that the man moves backward.

Thus, his final velocity ends up being 0.187 m/s backward.

Answer:

The beats frequency measures approximately

4.4 kHz

Explanation:

The beat frequency arises from the original ultrasound frequency, , and the frequency of the sound reflected off the car, :

(1)

To calculate the frequency of the reflected sound, we apply the Doppler effect formula:

where

v = 340 m/s, the speed of sound

is the velocity of the car

is the frequency of the sound emitted

By substituting values,

Thus, the beat frequency (1) is

Since you've completed parts a and b, I will tackle part c.
For part C
To respond to this question, we must identify the zeros of the velocity function:

This polynomial can be factored:

Finding the zeros now becomes straightforward since the function equals zero when any factor is zero.

By solving these equations, we identify our zeros:

The particle remains stationary at t=0 and t=3/2.
For part D
We must discover when the velocity function exceeds zero. We will utilize its factored form.
We will assess when each factor is greater than zero and compile the findings in the following table:

From the table, it's evident that our function is positive when and t>3/2.
This indicates the interval during which the particle moves forward.
For part E
The distance traveled can be represented as:

We simply substitute t=12 to calculate the total distance traveled:

For part F
Acceleration is defined as the rate at which velocity changes.
We determine acceleration by deriving the velocity function concerning time.

To find the acceleration at 1 second, we substitute t=1s into the previous equation: