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myrzilka [38]
3 years ago
7

Cliff divers at Acapulco jump into the sea from a cliff 36 meters high. At the level of the sea, there is an outcropping of rock

that sticks out a horizontal distance of 6 meters. With what minimum horizontal velocity must the cliff divers leave the top of the cliff if they are to miss this rocky outcropping?
Physics
1 answer:
Harrizon [31]3 years ago
3 0

Answer:

<em>The cliff drivers must leave the top of the cliff at 2.21 m/s</em>

Explanation:

<u>Horizontal Motion</u>

When an object is thrown horizontally with a speed v from a height h, it describes a curved path ruled exclusively by gravity until it eventually hits the ground.

The range or maximum horizontal distance traveled by the object can be calculated as follows:

\displaystyle d=v\cdot\sqrt{\frac  {2h}{g}}

If the range is known and we are required to find the initial speed of launch, then we can solve the above equation for v as follows:

\displaystyle v=d\cdot\sqrt{\frac  {g}{2h}}

Cliff drivers jump into the sea from a height of h=36 m and must pass over an obstacle d=6 meters away from the cliff.

Let's calculate the speed needed:

\displaystyle v=6~m\cdot\sqrt{\frac  {9.8~m/s^2}{2\cdot 36~m}}

\displaystyle v=6~m\cdot\sqrt{\frac  {9.8~m/s^2}{72~m}}

v=2.21~m/s

The cliff drivers must leave the top of the cliff at 2.21 m/s

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A hollow cylinder with an inner radius of 5 mm and an outer radius of 26 mm conducts a 4-A current flowing parallel to the axis
bearhunter [10]

Answer:

B = 38.2μT

Explanation:

By the Ampere's law you have that the magnetic field generated by a current, in a wire, is given by:

B=\frac{\mu_o I_r}{2\pi r}     (1)

μo: magnetic permeability of vacuum = 4π*10^-7 T/A

r: distance from the center of the cylinder, in which B is calculated

Ir: current for the distance r

In this case, you first calculate the current Ir, by using the following relation:

I_r=JA_r

J: current density

Ar: cross sectional area for r in the hollow cylinder

Ar is given by  A_r=\pi(r^2-R_1^2)

The current density is given by the total area and the total current:

J=\frac{I_T}{A_T}=\frac{I_T}{\pi(R_2^2-R_1^2)}

R2: outer radius = 26mm = 26*10^-3 m

R1: inner radius = 5 mm = 5*10^-3 m

IT: total current  = 4 A

Then, the current in the wire for a distance r is:

I_r=JA_r=\frac{I_T}{\pi(R_2^2-R_1^2)}\pi(r^2-R_1^2)\\\\I_r=I_T\frac{r^2-R_1^2}{R_2^2-R_1^2}  (2)

You replace the last result of equation (2) into the equation (1):

B=\frac{\mu_oI_T}{2\pi r}(\frac{r^2-R_1^2}{R_2^2-R_1^2})

Finally. you replace the values of all parameters:

B=\frac{(4\pi*10^{-7}T/A)(4A)}{2\PI (12*10^{-3}m)}(\frac{(12*10^{-3})^2-(5*10^{-3}m)^2}{(26*10^{-3}m)^2-(5*10^{-3}m)^2})\\\\B=3.82*10^{-5}T=38.2\mu T

hence, the magnitude of the magnetic field at a point 12 mm from the center of the hollow cylinder, is 38.2μT

8 0
2 years ago
(4%) Problem 9: A mass is connected to a spring and is allowed to move horizontally. The mass is at a position L when the spring
skad [1K]

Answer:

a) Acceleration is zero , c)   Speed ​​is cero

Explanation:

a) the equation that governs the simple harmonic motion is

         x = A cos (wt +φφ)

Where A is the amplitude of the movement, w is the angular velocity and φ the initial phase determined by the initial condition

Body acceleration is

         a = d²x / dt²

Let's look for the derivatives

         dx / dt = - A w sin (wt + φ)

         a = d²x / dt² = - A w² cos (wt + φ)

In the instant when it is not stretched x = 0

As the spring is released at maximum elongation, φ = 0

            0 = A cos wt

            Cos wt = 0         wt = π / 2

Acceleration is valid for this angle

           a = -A w² cos π/2 = 0

Acceleration is zero

b)

c) When the spring is compressed x = A

Speed ​​is

             v = dx / dt

             v = - A w sin wt

We look for time

            A = A cos wt

            cos wt = 1         wt = 0, π

For this time the speedy vouchers

            v = -A w sin 0 = 0

Speed ​​is cero

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umka2103 [35]

Answer:

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Identify two size dependent properties and two size independent properties of an iron nail
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2 size dependent = volume and mass. 2 size independent properties = conductivity, bowing point, state of matter, and melting point. analyze, name two size dependent properties and two size independent properties of an iron nail.


hope this helps

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3 years ago
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What ramp angle would produce an acceleration of 2 m/s2 for a cart rolling down? Assume no friction and that the angle is measur
r-ruslan [8.4K]
From Newton's second law:
a = F/mass
Therefore, acceleration of an object rolling a ramp would be:
a = g(sin theta) - friction coefficient (g) (sin theta)
The negative sine is due to the kinetic energy opposing the gravity

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Substituting in the equation, we get:
2 = 9.8 sin(theta)
sin (theta) = 0.20408
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3 years ago
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