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
nordsb [41]
2 years ago
8

A clever inventor has created a device that can launch water balloons with an initial speed of 85.0 m/s. Her goal is to pass a b

alloon through a small hoop mounted on the observation platform at the top of the Eiffel Tower, 276 m above the ground. If the balloon is to pass through the hoop at the peak of its flight, at what angle above horizontal should she launch the balloon? Please explain step by step

Physics
1 answer:
seropon [69]2 years ago
6 0

Answer:

She should launch the balloon at an angle of 59.9° above the horizontal.

Explanation:

Please, see the attached figure for a graphical description of the problem.

The position and velocity vectors of the water balloon at time "t" can be obtained using the following equations:

r = (x0 + v0 · t · cos θ, y0 + v0 · t · sin θ + 1/2 · g · t²)

v = (v0 · cos θ, v0 · sin θ + g · t)

Where:

r = position vector at time "t".

x0 = initial horizontal position.

v0 = initial velocity.

t = time.

θ = launching angle.

y0 = initial vertical position.

g = acceleration due to gravity (-9.81 m/s² considering the upward direction as positive).

v = velocity vector at time "t".

Let´s place the origin of the frame of reference at the launching point so that x0 and y0 = 0.

At the maximum height (276 m), the vector velocity of the balloon is horizontal (see v1 in the figure). That means that the y-component of the velocity vector is 0. Then, using the equation of the y-component of the velocity vector, we can write:

At maximum height:

vy = v0 · sin θ + g · t

0 = v0 · sin θ + g · t

We also know that at maximum height, the y-component of the position vector is 276 m (see r1y in the figure). Then:

At maximum height:

y = y0 + v0 · t · sin θ + 1/2 · g · t²  

276 m = y0 + v0 · t · sin θ + 1/2 · g · t²

So, we have two equations with two unknowns (θ and t):

276 m = y0 + v0 · t · sin θ + 1/2 · g · t²

0 = v0 · sin θ + g · t

To solve the system of equations, let´s take the equation of the y-component of the velocity and solve it for sin θ. Then, we will replace sin θ in the equation of the y-component of the position to obtain the time and finally obtain θ:

0 = v0 · sin θ + g · t

0 = 85.0 m/s · sin θ - 9.81 m/s² · t

9.81 m/s² · t / 85.0 m/s = sin θ

Replacing sin θ in the equation of the vertical component of the position:

276 m = y0 + v0 · t · sin θ + 1/2 · g · t²    (y0 = 0)

276 m = 85.0 m/s · t · (9.81 m/s² · t /85. 0 m/s) - 1/2 · 9.81 m/s² · t²

276 m = 9.81 m/s² · t² - 1/2 · 9.81 m/s² · t²

276 m = 1/2 · 9.81 m/s² · t²

276 m / ( 1/2 · 9.81 m/s²) = t²

t = 7.50 s

Now, we can calculate the angle θ using the equation obtained above:

9.81 m/s² · t / 85.0 m/s = sin θ

9.81 m/s² · 7.50 s / 85.0 m/s = sin θ

θ = 59.9°

She should launch the balloon at an angle of 59.9° above the horizontal.

You might be interested in
How old is the universe
Virty [35]
Roughly 13.8 billion years old according to science
5 0
2 years ago
Read 2 more answers
A spring vibrates 120 times in 2 mins find its frequency and time period​
german

2 minutes is 120 seconds, so if you were finding vibrations per minute, it would be 60 times a minute.

3 0
2 years ago
The layer of the Earth that is composed of large plates that interlock and move over time is the _______. asthenosphere lithosph
siniylev [52]
The lithosphere because it includes the outer region of the earth including the crust and outer mantle
4 0
2 years ago
Read 2 more answers
Compare between chromosphere, corona and photosphere
gladu [14]

Answer:

Explained

Explanation:

Photosphere: The lowest layer of the sun is called photo sphere . It is about 300 miles thick from the surface. It is the source of solar flares. It is  marked by bright bubbling granules of plasma.

chromosphere emits a reddish glow as the super heated hydrogen burns off but the red rim can only be seen during total solar eclipse.

The third layer of the sun atmosphere is Corona. It can also only be seen during during a total solar eclipse. Temperature in corona can reach as high as 3.5 million degree fahrenheit.  As the gases cool they become solar winds.

5 0
3 years ago
Light travels at a speed of close to 3 x 10^5 km/s in vacuum. Given that it takes light 8 min and 19 s to travel the distance fr
never [62]

Answer:

1497×10⁵ km

Explanation:

Speed of light in vacuum = 3×10⁵ km/s

Time taken by the light of the Sun to reach the Earth = 8 min and 19 s

Converting to seconds we get

8×60+19 = 499 seconds

Distance = Speed × Time

\text{Distance}=3\times 10^5\times 499\\\Rightarrow \text{Distance}=1497\times 10^5\ km

1 AU = 1497×10⁵ km

The Sun is 1497×10⁵ km from Earth

8 0
3 years ago
Other questions:
  • Which of the following molecules is correctly paired with its macromolecule class? (2 points)
    8·1 answer
  • If you have 500 g of water at 25oc and wish to heat it to 74o c, what is the specific heat of water
    14·1 answer
  • A 32-cm-long solenoid, 1.8 cm in diameter, is to produce a 0.30-T magnetic field at its center. If the maximum current is 4.5 A,
    11·1 answer
  • Help with 5-10 please
    5·1 answer
  • After a parallel-plate capacitor has been fully charged by a battery, the battery is disconnected and the plate separation is in
    9·2 answers
  • A star is estimated to be 4.8 x 10^15 kilometers away from the earth. When we see this star in the night sky, how old is this im
    5·2 answers
  • What creates the changes in step 1,2,3 of the nitrogen cycle
    9·1 answer
  • A ball rolls off a table and it traveling with a horizontal velocity of 2 m/s and 1 point
    15·2 answers
  • Pls help. This is about heat. I got the answer, just need the working
    8·1 answer
  • A sound with a lot of energy is ____________________ than a sound with less energy.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!