A spring-loaded gun, fired vertically, shoots a marble 9.0 m straight up in the air. What is the marble's range if it is fired horizontally from 1.8 m above the ground?

Answers

Answer 1

Answer:

Final answer:

The range of the marble when fired horizontally from 1.8m above the ground can be calculated using the equations of motion in physics. First, the time of flight is found using the vertical motion and then the range is calculated using the time of flight and the initial velocity determined from the vertical launch. The marble's range is approximately 8.4m.

Explanation:

To solve this problem, we need to make use of the concept of projectile motion in physics. The most crucial part in solving this type of problem is to break the motion into its horizontal and vertical components.

First, we find the time the projectile is in the air using the vertical motion. Ignoring air resistance, the time a projectile is in the air is determined by the initial vertical velocity and the height from which it drops. Here, the height is given as 1.8m and we can use the equation h = 0.5gt^2, where h is the height, g is the acceleration due to gravity (9.8 m/s^2), and t is the time. After calculating, we find that the time the marble is in the air is about 0.6 seconds.

Now, we can use the time to find the horizontal distance traveled by the marble, a.k.a the range. The range is given by R = vt, where v is the horizontal velocity, which is the same as the initial vertical velocity. From the problem, we know the marble reached a height of 9.0m when shot vertically, which we can use to find the initial velocity using the equation v = sqrt(2gh), where g is the acceleration due to gravity (9.8 m/s^2) and h is the height. We find that the initial velocity is about 14 m/s.

So, the range R = vt = 14m/s * 0.6s = 8.4m. Therefore, the marble's range when fired horizontally from 1.8m above the ground is approximately 8.4m.

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24-gauge copper wire has a diameter of 0.51 mm. The speaker is located exactly 4.27 m away from the amplifier. What is the minimum resistance of the connecting speaker wire at 20°C? Hint: How many wires are required to connect a speaker!Compare the resistance of the wire to the resistance of the speaker (Rsp = 8 capital omega)

Answers

Answer:

R = 8.94 10⁻² Ω/m, R_sp / R_total = 44.8

Explanation:

The resistance of a metal cable is

R = ρ L / A

The area of a circle is

A = π R²

The resistivity of copper is

ρ = 1.71 10⁻⁸ ohm / m

Let's calculate

R = 1.71 10⁻⁸ 4.27 / (π (0.51 10⁻³)²)

R = 8.94 10⁻² Ω/m

Each bugle needs two wire, phase and ground

The total wire resistance is

R_total = 2 R

R_total = 17.87 10⁻² Ω

Let's look for the relationship between the resistance of the bugle and the wire

R_sp / R_total = 8 / 17.87 10⁻²

R_sp / R_total = 44.8

Final answer:

The resistance of the speaker wire can be calculated using the formula for the resistance of a wire, taking into account the resistivity of copper, the length and thickness of the wire, and whether a single or pair of wires is used.

Explanation:

The question is asking you to find the minimum resistance of a copper wire given its diameter and length, plus the resistance of the speaker it's connected to. Resistance of a wire is calculated using the formula R=ρL/A, where R is the resistance, ρ (rho) is the resistivity of the material (in this case, copper), L is the length of the wire, and A is the cross-sectional area of the wire.

First, you need to find the area of the 0.51 mm diameter wire. The area (A) of a wire is given by the formula π(d/2)^2 where d is the diameter of the wire. After calculating the area, use the formula R=ρL/A to calculate the resistance. For copper wire at 20°C, ρ is approximately 1.68 × 10^-8 Ω·m. Substituting these values into the formula will give you the resistance of the wire in ohms.

Note: you may need to consider whether you have just a single wire or a pair, since two wires are typically required to connect a speaker. If a pair is used, each wire will carry half the current, which affects the total resistance.

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The production of heat by metabolic processes takes place throughout the volume of an animal, but loss of heat takes place only at the surface (i.e. the skin). Since heat loss must be balanced by heat production if an animal is to maintain a constant internal temperature, the relationship between surface area and volume is relevant for physiology. If the surface area of a cube is increased by a factor of 2, by what factor does the volume of the cube change? Give your answer to two significant figures. 1.59

Answers

To solve this problem we will apply the concepts related to the change in length in proportion to the area and volume. We will define the states of the lengths in their final and initial state and later with the given relationship, we will extrapolate these measures to the area and volume

The initial measures,

$\text{Initial Length} = L$

$\text{Initial surface Area} = 6L^2$ (Surface of a Cube)

$\text{Initial Volume} = L^3$

The final measures

$\text{Final Length} = L_f$

$\text{Final surface area} = 6L_f^2$

$\text{Final Volume} = L_f^3$

Given,

$((SA)_f)/((SA)_i) = 2$

Now applying the same relation we have that

$((L_f)/(L_i))^2 = 2$

$(L_f)/(L_i) = √(2)$

The relation with volume would be

$((Volume)_f)/((Volume)_i) = ((L_f)/(L_i))^3$

$((Volume)_f)/((Volume)_i) = (√(2))^3$

$((Volume)_f)/((Volume)_i) = (2√(2))$

$((Volume)_f)/((Volume)_i) = 2.83$

Volume of the cube change by a factor of 2.83

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

Answers

Answer:

Explanation:

The mass balance is an application of conservation of mass, to the analysis of physical system. This is given in an equation form as

Input = Output + Accumulation

The conservation law that is used in this analysis of the system actually depends on the context of the problem. Nevertheless, they all revolve around conservation of mass. By conservation of mass, I mean that the fact that matter cannot disappear or be created spontaneously.

A rock is thrown from the top of a building 146 m high, with a speed of 14 m/s at an angle 43 degrees above the horizontal. When it hits the ground, what is the magnitude of its velocity (i.e. its speed).

Answers

Answer:

time is 32 s and speed is 304.3 m/s

Explanation:

Height, h = 146 m

speed, u = 14 m/s

Angle, A = 43 degree

Let it hits the ground after time t.

Use second equation of motion

$h = u t +0.5 at^2\n\n- 146 =14 sin 43 t - 4.9 t^2\n\n4.9 t^2 - 9.5 t - 146 =0 \n\nt =\frac{9.5\pm\sqrt {90.25 + 2861.6}}{9.8}\n\nt=(9.5\pm 54.3)/(9.8)\n\nt = 32.05 s, - 22.4 s$

Time cannot be negative so the time is t = 32 s .

The vertical velocity at the time of strike is

v' = u sin A - g t

v' = 14 sin 43 - 9.8 x 32 = 9.5 - 313.6 = - 304.1 m/s

horizontal velocity

v'' = 14 cos 43 =10.3 m/s

The resultant velocity at the time of strike is

$v=√(v'^2 + v''^2)\n\nv = √(304.1^2 +10.3^2 )\n\nv = 304.3 m/s$

3.what does this stand for ??

Answers

Answer:

see below

Explanation:

The triangle stands for the change in

We would change the change in x

Answer:

ΔThis is the symbol of Delta which means Change

and x is length/distance/position.

Thus,Δxstands for Change in length/distance/position.

-TheUnknownScientist

A dynamics cart with a friction pad is placed at the top of an inclined track and released fromrest. The cart accelerates down the incline at a rate of 0.60 m/s2. If the track is angled at 10degrees above the horizontal, determine the coefficient of kinetic friction between the cart andthe track.

Answers

Answer:

0.114

Explanation:

There are two forces acting on the cart in the direction along the cart:

- The component of the gravitational force in the direction parallel to the ramp, $mg sin \theta$ , down along the ramp

- The force of friction, $\mu N$ , up along the ramp

So the equation of motion along this direction is:

$mg sin \theta - \mu N = ma$ (1)

where

m is the mass of the cart

$g=9.8 m/s^2$ is the acceleration due to gravity

$\theta=10^(\circ)$ is the angle of the ramp

$\mu$ is the coefficient of kinetic friction

N is the normal force exerted by the ramp on the cart

$a=0.60 m/s^2$ is the acceleration of the cart

The normal force can be found from the equation of the forces along the direction perpendicular to the ramp; in fact, the normal force is balanced by the component of the weight perpendicular to the ramp, so we have:

$N-mg cos \theta = 0$

From which we get:

$N=mg cos \theta$

Substituting into (1),

$mg sin \theta - \mu mg cos \theta = ma$

And solving for $\mu$ , we find the coefficient of friction:

$\mu = (g sin \theta - a)/(g cos \theta)=((9.8)(sin10^(\circ))-0.60)/((9.8)(cos 10^(\circ))=0.114$

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A diverging lens has a focal length of -30.0 cm. An object is placed 18.0 cm in front of this lens.(a) Calculate the image distance.(b) Calculate the magnification.

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Crude oil is a mixture of many different components. The extraction of crude oil from the Earth is important, but its refinement into different substances is a key piece to obtaining as many uses as possible from the crude oil. Using the diagram, justify the source of data used to develop the technology for refining the crude oil.