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Assuming a vertical trajectory with no drag, derive the applicable form of the rocket equation for this application

Answers

Answer 1
Answer:

Answer:

The vertical trajectory is governed by Ordinary Differential Equation.

Time derivatives of each state variables.

d(d)/dt = v, d(m)/dt = -d(m-fuel)/dt, d(v)/dt = F/m.

Where V is velocity positive upwards, t is time, m is mass, m-fuel is fuel mass, F is Total force, positive upwards.

Therefore,

F = -mg - D + T, If V is positive and

F = -mg + D - T, If T is negative.

D is drag and the questions gave it as zero.

Explanation:

The two sign cases in derivative equations above are required because F is defined positive up, so the drag D and thrust T can subtract or add to F depending in the sign of V . In contrast, the gravity force contribution mg is always negative. In general, F will be some function of time, and may also depend on the characteristics of the particular rocket. For example, the T component of F will become zero after all the fuel is expended, after which point the rocket will be ballistic, with only the gravity force and the aerodynamic drag force being p

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In an evironmental system of subsystem, the mass balance equation is:__________.

Each shot of the laser gun most favored by Rosa the Closer, the intrepid vigilante of the lawless 22nd century, is powered by the discharge of a 1.89 Fcapacitor charged to 60.9 kV. Rosa rightly reckons that she can enhance the effect of each laser pulse by increasing the electric potential energy of the charged capacitor. She could do this by replacing the capacitor's filling, whose dielectric constant is 431, with one possessing a dielectric constant of 947.Required:
a. Find the electric potential energy of the original capacitor when it is charged. (in Joules)
b. Calculate the electric potential energy of the upgraded capacitor when it is charged. ( In Joules)

Answers

Answer:

a

U  =  3.505 *10^9 \  J

b

U_1 = 7.696 *10^9 \ J

Explanation:

From the question we are told that

The capacitance is C = 1.89 \ F

The voltage is V = 60.9 \ k V = 60.9 *10^(3) \ V

The first dielectric constant is \epsilon_1 = 431

The second dielectric constant is \epsilon_2 = 947

Generally the electric potential energy is mathematically represented as

U = (1)/(2) * C * V^2

=> U = (1)/(2) * 1.89 * (60.9 *10^(3))^2

=> U = 3.505 *10^9 \ J

Generally the capacitance when the capacitor's filling was changed is

C_n = 1.89 * (947)/(431)

=>   C_n  =  4.15

Generally the electric potential energy when the capacitor's filling  was changed is

       U_1  =  (1)/(2)  *  C_1  * V^2

=>  U_1  =  (1)/(2)  *   4.15  * (60.9 *10^(3))^2

=>  U_1  = 7.696 *10^9 \  J

A person pushing a stroller starts from rest, uniformly accelerating at a rate of 0.500 m/s2. What is the velocityof the stroller after it has traveled 6.32 m?

Answers

You're going to use the constant acceleration motion equation for velocity and displacement:

(V)final² = (V)initial²+2a(dx)

Given:

a=0.500m/s²

dx=6.32 m

(V)intial=0m

(V)final= UNKNOWN

(V)final= 2.51396m/s

An alternating current is supplied to an electronic component with a rating that the voltage across it can never, even for an instant, exceed 16 V. What is the highest rms voltage that can be supplied to this component while staying below the voltage limit?A)8 sqrt 2 V

B) 16 sqrt 2 V

C) 256 V

D) 8

Answers

Answer:

A) V_(rms)=8√(2) V

Explanation:

Maximum voltage =V_(max)=16 V

Maximum voltage and rms voltage are related to each other by

V_(max)=V_(rms) * √(2) \nV_(rms)=(V_(max))/( √(2))\nV_(rms)=(16)/(√(2)) \nV_(rms)=8√(2) V

1. A bicyclist starts at 2.5 m/s and accelerates along a straight path to a speed of 12.5 m/s ina time of 4.5 seconds. What is the bicyclist's acceleration to the nearest tenth of a m/s??

Answers

Answer:

2.2m/s

Explanation:

a=v-u/t

12.5-2.5/4.5=2.222

~2.2m/s

The height h (in feet) of an object shot into the air from a tall building is given by the function h(t) = 650 + 80t − 16t2, where t is the time elapsed in seconds. (a) Write a formula for the velocity of the object as a function of time t.

Answers

Answer:

80 - 32t

Explanation:

The height, h, in terms of time, t, is given as:

h(t) = 650 + 80t − 16t²

Velocity is the derivative of distance with respect to time:

v(t) = dh(t)/dt = 80 - 32t

Final answer:

The velocity of the object as a function of time is given by the derivative of the height function, which is v(t) = 80 - 32t.

Explanation:

The height h(t) of an object is given by the equation h(t) = 650 + 80t − 16t2. To find the velocity v(t), we need to take the derivative of h(t) with respect to time t. Using the power rule, we get:

v(t) = dh/dt = 0 + 80 - 32t.

So, the velocity of the object as a function of time t is v(t) = 80 - 32t.

Learn more about Velocity Function here:

brainly.com/question/33157131

#SPJ11

A long, thin solenoid has 450 turns per meter and a radius of 1.17 cm. The current in the solenoid is increasing at a uniform rate did. The magnitude of the induced electric field at a point which is near the center of the solenoid and a distance of 3.45 cm from its axis is 8.20×10−6 V/m.Calculate di/dt
di/dt = _________.

Answers

The value of di/dt from the given values of the solenoid electric field is;

di/dt = 7.415 A/s

We are given;

Number of turns; N = 450 per m

Radius; r = 1.17 cm = 0.0117 m

Electric Field; E = 8.2 × 10⁻⁶ V/m

Position of electric field; r' = 3.45 cm = 0.0345 m

According to Gauss's law of electric field;

∫| E*dl | = |-d∅/dt |

Now, ∅ = BA = μ₀niA

where;

n is number of turns

i is current

A is Area

μ₀ = 4π × 10⁻⁷ H/m

Thus;

E(2πr') = (d/dt)(μ₀niA)  (negative sign is gone from the right hand side because we are dealing with magnitude)

Since we are looking for di/dt, then we have;

E(2πr') = (di/dt)(μ₀nA)

Making di/dt the subject of the formula gives;

di/dt = E(2πr')/(μ₀nA)

Plugging in the relevant values gives us;

di/dt = (8.2 × 10⁻⁶ × 2 × π × 0.0345)/(4π × 10⁻⁷ × 450 × π × 0.0117²)

di/dt = 7.415 A/s

Read more at; brainly.com/question/14003638

Answer:

(di)/(dt) = 7.31 \ A/s

Explanation:

From the question we are told that  

     The  number of turns is  N = 450 \ turns

      The  radius is  r = 1.17 \ cm = 0.0117 \ m

       The  position from the center consider is  x =  3.45 cm  =  0.0345 m

       The  induced emf is  e = 8.20 *10^(-6) \ V/m

Generally according to Gauss law

        \int\limits { e } \, dl = \mu_o * N * (di)/(dt ) * A

=>    e * 2\pi x = \mu_o * N * (d i )/(dt ) * A

Where A is the  cross-sectional area of the solenoid which is mathematically represented as

                A = \pi r ^2

=>      e * 2\pi x = \mu_o * N * (d i )/(dt ) * \pi r^2

=>       (di)/(dt) = (2e * x )/(\mu_o * N * r^2)ggl;

Here  \mu_o is the permeability of free space with value

          \mu_o = 4\pi * 10^(-7) \ N/A^2

=>     (di)/(dt) = (2 * 8.20*10^(-6) * 0.0345 )/( 4\pi * 10^(-7) * 450 * (0.0117)^2)

=>      (di)/(dt) = 7.31 \ A/s
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