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A hot-air balloon is descending at a rate of 2.3 m>s when a pas- senger drops a camera. If the camera is 41 m above the ground when it is dropped, (a) how much time does it take for the cam- era to reach the ground, and (b) what is its velocity just before it lands? Let upward be the positive direction for this problem.

Answers

Answer 1

Answer:

(a) It takes approximately 2.8956 seconds for the camera to reach the ground.

(b) The velocity of the camera just before it lands is approximately -28.375 m/s (downward).

We have,

Given information:

Initialheight (h₀) = 41 m (above the ground)

Descentrate of the hot-air balloon = -2.3 m/s (negative because it's descending)

We can use the kinematicequations to solve for the time it takes for the camera to reach the ground and its velocity just before landing.

(a)

To find the time it takes for the camera to reach the ground, we can use the following kinematic equation:

h = h₀ + (v₀)t + (1/2)at²

Where:

h = final height (0 m, as it reaches the ground)

h₀ = initial height (41 m)

v₀ = initial velocity (0 m/s, as the camera is dropped)

a = acceleration (acceleration due to gravity, approximately -9.8 m/s²)

t = time (what we're solving for)

Plugging in the values:

0 = 41 + (0)t + (1/2)(-9.8)t²

Simplifying:

-4.9t² = 41

Divide by -4.9:

t² = -41 / -4.9

t² = 8.36734694

Taking the square root:

t = √8.36734694

t ≈ 2.8956 seconds

(b)

To find the velocity just before the camera lands, we can use the following kinematic equation:

v = v₀ + at

Where:

v = final velocity (what we're solving for)

v₀ = initial velocity (0 m/s)

a = acceleration (acceleration due to gravity, -9.8 m/s²)

t = time (2.8956 seconds, calculated in part a)

Plugging in the values:

v = 0 + (-9.8)(2.8956)

v ≈ -28.375 m/s

The negativesign indicates that the velocity is directed downward, which is consistent with the descending motion.

Thus,

(a) It takes approximately 2.8956 seconds for the camera to reach the ground.

(b) The velocity of the camera just before it lands is approximately -28.375 m/s (downward).

Learn more about kinematicsequations here:

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On a map each inch represents 25 miles what is the length of a highway if it is 6 inches long on a map

Answers

Answer:

150 hope this helps

Explanation:

Answer:

150

Explanation:

As you go up the y-axis, what happens to the number of sprouted bean seeds?A. Sprouted bean seeds decrease.

B. Sprouted bean seeds increase.

C. Sprouted bean seeds remain constant.

D. None of the above

Answers

As we go up the y-axis, the number of sproutedbean seeds increase (option B).

What is a graph?

Graph is a data chart intended to illustrate the relationship between a set (or sets) of numbers (quantities, measurements or indicative numbers) and a reference set.

In a graph, there are two axes as follows;

Y-axis or vertical axis
X-axis or horizontal axis

According to this question, a graph of number of sprouted bean seeds on the y-axis is plotted against temperature on the x-axis.

We can observe that as we go up the y-axis, the number of sprouted bean seeds increase.

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A mysterious object with a surface area of 0.015 m2, volume of 0.000125 m3, density of 100 kg/m3, specific heat of 100 J/(kgK), thermal conductivity of 2 W/(mK), with an unknown initial temperature was placed in a fluid with a density of 50 kg/m3, specific heat of 70 J/(kgK), thermal conductivity of 0.1 W/(mK), at a temperature of 400K. The heat transfer coefficient is given to be 10 W/(m2K). After 10 seconds, the temperature of the object is measured to be 380K. Determine the object's initial temperature.

Answers

Answer:

The object's initial temperature is 333.6 K

Explanation:

We first assume that the liquid can only transfer heat to the object through convective heat transfer method.

Let T₀ = the initial temperature of the object

T = temperature of the object at anytime.

The rate of heat transfer from the liquid to the object is given as

Q = -hA (T∞ - T)

T∞ = temperature of the fluid = 400 K

A = Surface area of the object in contact with the liquid = 0.015 m²

h = Convective heat transfer coefficient is given to be = 10 W/(m²K)

The rate of heat gained by the object is given by

mC (d/dt)(T∞ - T)

m = mass of the object = ρV

ρ = density of the object = 100 kg/m³

V = volume of the object = 0.000125 m³

m = ρV = 100 × 0.000125 = 0.0125 kg

C = specific heat capacity of the object = 100 J/(kgK)

The rate of heat loss by the liquid = rate of heat gain by the object

-hA (T∞ - T) = mC (d/dt)(T∞ - T)

(d/dt)(T∞ - T) = - (dT/dt) ( Since T∞ is a constant)

- mC (dT/dt) = -hA (T∞ - T)

(dT/dt) = (hA/mC) (T∞ - T)

Let s = (hA/mC)

(dT/dt) = -s (T - T∞)

dT/(T - T∞) = -sdt

Integrating the left hand side from T₀ (the initial temperature of the object) to T and the right hand side from 0 to t

In [(T - T∞)/(T₀ - T∞)] = -st

(T - T∞)/(T₀ - T∞) = e⁻ˢᵗ

(T - T∞) = (T₀ - T∞)e⁻ˢᵗ

s = (hA/mC) = (10 × 0.015)/(0.0125×100) = 0.12

T = 380 K at t = 10 s

T₀ = ?

T∞ = 400 K

st = 0.12 × 10 = 1.2

(380 - 400) = (T₀ - 400) e⁻¹•²

(-20/0.3012) = (T₀ - 400)

(T₀ - 400) = - 66.4

T₀ = 400 - 66.4 = 333.6 K

Hope this Helps!!!

A proton and an alpha particle (helium nucleus consisting of two protons and two neutrons) are accelerated from rest across the same potential difference. Assume the proton mass and the neutron mass are roughly the same and neglect any relativistic effect. Compared to the final speed of the proton, the final speed of the alpha particle is?1. less by a factor of 22. less by a factor of √ 23. less by a factor of 44. greater by a factor of 25. the same

Answers

Answer:

option B

Explanation:

we know,

change in energy is equal to

$W = (1)/(2)m(v^2 - u^2)$

$W = (1)/(2)m(v^2 - 0^2)$

$W = (1)/(2)m v^2$

$q = (1)/(2)m v^2$

proton mass and the neutron mass are roughly the same

so,

$q \alpha m v^2$

now,

$(q_p)/(q_(\alpha)) = (m_p v_p^2)/(m_(\alpha)v_(\alpha)^2)$

$(q_p)/(q_(\alpha)) = (m_p v_p^2)/(2 m_pv_(\alpha)^2)$

we know,

mass of alpha particle is four times mass of the mass of proton.

mα = 4 m_p

$(e)/(2e) = ( v_p^2)/(4 v_(\alpha)^2)$

$( v_p^2)/(v_(\alpha)^2) = 2$

$v_(\alpha)^2 =( v_p^2)/(2)$

$v_(\alpha)=( v_p)/(√(2))$

less by a factor of √2

Hence, the correct answer is option B

Much of our knowledge of the interior of the Earth comes from the study of planetary vibrations, which is the science of

Answers

Answer:

Seismology.

Explanation:

Seismology is the beach of physical science that deals with the study of vibrations that comes out from the interior of the earth onto the surface and these vibrations are in the form of seismic waves that are primary, secondary, and surface waves.

The science of seismology tells about the magnitude and intensity of these waves that lead to planetary vibrations. These waves trigger earthquakes, floods, and even landslides.

Select the correct answer.Which statement is true if the refractive index of medium A is greater than that of medium B?
A.
O B.
Total internal reflection is possible when light travels from air to medium B to medium A.
Total internal reflection is possible when light travels from medium A to medium B.
Total internal reflection is possible when light travels from medium B to medium A.
D. Total internal reflection is possible when light travels from air to medium A.
E. Total internal reflection is possible when light travels from air to medium B.
C
C.

Answers

Final answer:

If the refractive index of medium A is greater than that of medium B, then total internal reflection is possible when light travels from medium B to medium A.

Explanation:

If the refractive index of medium A is greater than that of medium B, then total internal reflection is possible when light travels from medium B to medium A.

Learn more about Refraction of light

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