1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Solnce55 [7]
2 years ago
10

You have been hired as a technical consultant for an early-morning cartoon series for children to make sure that the science is

correct. In the script, a wagon containing two boxes of gold (total mass of wagon and gold is 166 kg) has been cut loose from the horses by an outlaw. The wagon starts from rest 77 meters up a hill with a 8o slope. The outlaw plans to have the wagon roll down the hill and across the level ground and then crash into a canyon where his confederates wait. But in a tree 41 meters from the edge of the canyon wait the Lone Ranger (mass 65 kg) and Tonto (mass 66 kg). They drop vertically into the wagon as it passes beneath them. How long do the Lone Ranger and Tonto have to grab the gold and jump out of the wagon before the wagon heads over the cliff? You assume that the wagon rolls with negligible friction.
Physics
1 answer:
katen-ka-za [31]2 years ago
5 0

The initial potential energy of the wagon containing gold boxes will enable

it roll down the hill when cut loose.

The Lone Ranger and Tonto have approximately <u>5.1 seconds</u>.

Reasons:

Mass wagon and gold = 166 kg

Location of the wagon = 77 meters up the hill

Slope of the hill = 8°

Location of the rangers = 41 meters from the canyon

Mass of Lone Ranger, m₁ = 65 kg

Mass of Tonto m₂ = 66 kg

Solution;

Height of the wagon above the level ground, h = 77 m × sin(8°) ≈ 10.72 m

Potential energy = m·g·h

Where;

g = Acceleration due to gravity ≈ 9.81 m/s²

Potential energy of wagon, P.E. ≈ 166 × 9.81 × 10.72 = 17457.0912

Potential energy of wagon, P.E. ≈ 17457.0912 J

By energy conservation, P.E. = K.E.

K.E. = \mathbf{\dfrac{1}{2} \cdot m \cdot v^2}

Where;

v = The velocity of the wagon a the bottom of the cliff

Therefore;

\dfrac{1}{2} \times 166 \times v^2 = 17457.0912

v = \sqrt{\dfrac{17457.0912}{\dfrac{1}{2} \times 166} } \approx 14.5

Velocity of the wagon, v ≈ 14.5 m/s

Momentum = Mass, m × Velocity, v

Initial momentum of wagon = m·v

Final momentum of wagon and ranger = (m + m₁ + m₂)·v'

By conservation of momentum, we have;

m·v = (m + m₁ + m₂)·v'

\therefore v' = \mathbf{ \dfrac{m \cdot v}{(m + m_1 + m_2)  }}

Which gives;

\therefore v' = \dfrac{166 \times 14.5}{(166 + 65 + 66)  } \approx 8.1

The velocity of the wagon after the Ranger and Tonto drop in, v' ≈ 8.1 m/s

Time = \dfrac{Distance}{Velocity}

\mathrm{The \ time \ the\ Lone \  Ranger \  and  \ Tonto \  have,  \ t} = \dfrac{41 \, m}{8.1 \, m/s} \approx 5.1 \, s

The Lone Range and Tonto have approximately <u>5.1 seconds</u> to grab the

gold and jump out of the wagon before the wagon heads over the cliff.

Learn more here:

brainly.com/question/11888124

brainly.com/question/16492221

You might be interested in
19. After a snowstorm, you put on your frictionless skis and tie a rope to the back of your friend’s truck. Your total mass is 7
Kisachek [45]

Explanation:

It is given that,

Total mass is 70 kg

The truck exerts a constant force of 20 N.

Then the net force is given by :

F = ma

a is acceleration of rider

a=\dfrac{F}{m}\\\\a=\dfrac{20}{70}\\\\a=\dfrac{2}{7}\ m/s^2

Initial velocity of rider is 0. So, using equation of kinematics to find the final velocity as :

v=u+at\\\\v=at\\\\v=\dfrac{2}{7}\times 15\\\\v=4.28\ m/s

Since, 1 m/s = 2.23 mph

4.28 m/s = 9.57 mph

So, the speed of the rider is 4.28 m/s or 9.57 mph.  

5 0
3 years ago
If the baseball and the plastic ball were moving at the same speed which ball would hit a bat harder
Lerok [7]
A baseball would hit the bat harder. This is because the baseball is a lot heavier and more dense than the plastic ball. The keyword that you're looking for is density. The baseball is dense.
7 0
3 years ago
If the magnitude of the magnetic force on a proton is F when it is moving at 18.0 ∘ with respect to the field, what is the magni
Lelu [443]

Answer:

The force when θ = 33° is 1.7625 times of the force when θ = 18°

Explanation:

The force on a moving charge through a magnetic field is given by

F = qvB sin θ

q = charge of the moving particle

v = Velocity of the moving charge

B = Magnetic field strength

θ = angle between the magnetic field and the velocity (direction of the motion) of the moving charge

Because qvB are all constant, we can call the expression K.

F = K sinθ

when θ = 18°,

F = K sin 18° = 0.309K

when θ = 33°, let the force be F₁

F₁ = K sin 33° = 0.5446K

(F₁/F) = (0.5446K/0.309K) = 1.7625

F₁ = 1.7625 F

Hope this Helps!!!

5 0
3 years ago
Manufactured bolts can’t be too long or too short or they might not fit where they need to. Help determine which bolts will work
Sever21 [200]
What is the longest the bolt can be and still be acceptable
5 0
3 years ago
A swan on a lake gets airborne by flapping its wings and running on top of the water. If the swan must reach a velocity of 6.00
ira [324]

Answer:

A. 51.42 m.

B. 17.14 s.

Explanation:

Using equations of motion:

vf^2 = vi^2 + 2 * aS

Where,

vf = final velocity

a = acceleration

S = distance to which swan traveled

vi = 0 m/s

6.00^2 = 2 * 0.350S

S = 36/0.7

= 51.42 m.

B.

vf = vi + at

6 = 0 + 0.35t

t = 6/0.35

= 17.14 s.

5 0
3 years ago
Other questions:
  • What is the intensity in W/m2 of a laser beam used to burn away cancerous tissue that, when 85.0% absorbed, puts 470 J of energy
    5·1 answer
  • I need help fast!!!
    6·1 answer
  • the explorer visited the three places and raised her hand when she reached each of them, where would the change in gravitational
    6·2 answers
  • Explain the qualifications that must be met for any vehicle to go in space.
    15·2 answers
  • 2. The viscosity of a fluid is to be measured by an viscometer constructed of two 75–cm–long concentric cylinders. The outer dia
    7·1 answer
  • A man hits a 50 grams golf ball such that it leaves the tee at an angle of 40o with the horizontal and strikes the ground at the
    8·1 answer
  • A thin walled spherical shell is rolling on a surface. What
    8·1 answer
  • Write an essay on basketball history and how the game has changed over time
    6·1 answer
  • A plane is heading south with a velocity of 150 kilometers/hour. It experiences a tailwind with a velocity of 20 kilometers/hour
    13·2 answers
  • What is meant by the term 'total internal reflection'? (GCSE Level)
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!