The equation y = 2x + 3 represents the cost y (in dollars) of mailing a package that weighs x pounds.

A box with mass (m) it's sliding along on a friction-free surface at 9.87 m/s at a height of 1.81 meters. It travels down the hi

Rus_ich [418]

A) The answer is 11.53 m/s

The final kinetic energy (KEf) is the sum of initial kinetic energy (KEi) and initial potential energy (PEi).
KEf = KEi + PEi

Kinetic energy depends on mass (m) and velocity (v)
KEf = 1/2 m * vf²
KEi = 1/2 m * vi²

Potential energy depends on mass (m), acceleration (a), and height (h):
PEi = m * a * h

So:
KEf = KEi + PEi
1/2 m * vf² = 1/2 m * vi² + m * a * h
..
Divide all sides by m:
1/2 vf² = 1/2 vi² + a * h

We know:
vi = 9.87 m/s
a = 9.8 m/s²
h = 1.81 m

1/2 vf² = 1/2 * 9.87² + 9.8 * 1.81
1/2 vf² = 48.71 + 17.74
1/2 vf² = 66.45
vf² = 66.45 * 2
vf² = 132.9
vf = √132.9
vf = 11.53 m/s

b) The answer is 6.78 m

The kinetic energy at the bottom (KE) is equal to the potential energy at the highest point (PE)
KE = PE

Kinetic energy depends on mass (m) and velocity (v)
KE = 1/2 m * v²

Potential energy depends on mass (m), acceleration (a), and height (h):
PE = m * a * h

KE = PE
1/2 m * v² = m * a * h

Divide both sides by m:
1/2 * v² = a * h
v = 11.53 m/s
a = 9.8 m/s²
h = ?

1/2 * 11.53² = 9.8 * h
1/2 * 132.94 = 9.8 * h
66.47 = 9.8 * h
h = 66.47 / 9.8
h = 6.78 m

3 0

2 years ago

A wave will go faster through a liquid at ____________ temperatures

cupoosta [38]

<h3>Answer;</h3>

Higher temperatures

A wave will go faster through a liquid at higher temperatures

<h3>Explanation;</h3>

Mechanical waves are types of waves that require a material medium for transmission. An example of mechanical wave is the sound wave whose transmission occurs in medium such as solids, liquids and gases.

The transmission of mechanical waves involves vibration of particles through the medium of transmission, thus transfer of energy from one point to another. The vibration of particle may be in the form of a longitudinal wave or a transverse wave.

Increasing the temperature in a medium increases the kinetic energy of the particles in the medium and thus increasing the speed at which the particles vibrates and thus aiding a faster transmission of a wave.

7 0

3 years ago

Read 2 more answers

How much heat is required to convert 0.3 kg of ice at 0°C to water at the same temperature

madreJ [45]

Answer:

100,800 Jkg

The heat that is used to change the state of a mater is called latent heat.

In this case it is converting ice to water and it is called latent heat of fusion.

It is given by:

Heat = mc

where m is the mass of ice and l is the specific latent heat of fusion of ice.