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
zysi [14]
3 years ago
7

Gayle runs at a speed of 3.85 m/s and dives on a sled, initially at rest on the top of a frictionless snow-covered hill. After s

he has descended a vertical distance of 5.00 m, her brother, who is initially at rest, hops on her back and together they continue down the hill. What is their speed at the bottom of the hill if the total vertical drop is 15.0 m?
Physics
1 answer:
enot [183]3 years ago
6 0

Answer:

Final velocity at the bottom of hill is 15.56 m/s.

Explanation:

The given problem can be divided into four parts:

1. Use conservation of momentum to determine the speed of the combined mass (Gayle and sled)

From the law of conservation of momentum (perfectly inelastic collision), the combined velocity is given as:  

p_i = p_f  

m_1u_1 + m_2v_2 = (m_1 + m_2)v

v = \frac{(m_1u_1 + m_2v_2)}{(m_1 + m_2)}

v=\frac{[50.0\ kg)(3.85\ m/s) + 0]}{(50.0\ kg + 5.00\ kg)}= 3.5\ m/s  

2. Use conservation of energy to determine the speed after traveling a vertical height of 5 m.

The velocity of Gayle and sled at the instant her brother jumps on is found from the law of conservation of energy:  

E(i) = E(f)  

KE(i) + PE(i) = KE(f) + PE(f)  

0.5mv^2(i) + mgh(i) = 0.5mv^2(f) + mgh(f)  

v(f) = \sqrt{[v^2(i) + 2g(h(i) - h(f))]}

Here, initial velocity is the final velocity from the first stage. Therefore:  

v(f) = \sqrt{[(3.5)^2+2(9.8)(5.00-0)]}= 10.5\ m/s

3. Use conservation of momentum to find the combined speed of Gayle and her brother.  

Given:

Initial velocity of Gayle and sled is, u_1(i)=10.5 m/s

Initial velocity of her brother is, u_2(i)=0 m/s

Mass of Gayle and sled is, m_1=55.0 kg

Mass of her brother is, m_2=30.0 kg

Final combined velocity is given as:

v(f) = \frac{[m_1u_1(i) + m_2u_2(i)]}{(m_1 + m_2)}  

v(f)=\frac{[(55.0)(10.5) + 0]}{(55.0+30.0)}= 6.79 m/s  

4. Finally, use conservation of energy to determine the final speed at the bottom of the hill.

Using conservation of energy, the final velocity at the bottom of the hill is:  

E(i) = E(f)  

KE(i) + PE(i) = KE(f) + PE(f)  

0.5mv^2(i) + mgh(i) = 0.5mv^2(f) + mgh(f)  

v(f) = \sqrt{[v^2(i) + 2g(h(i) - h(f))]} \\v(f)=\sqrt{[(6.79)^2 + 2(9.8)(15 - 5.00)]}\\v(f)= 15.56\ m/s

You might be interested in
How do you measure the wavelength of wave?
Tasya [4]

Explanation:

by finding the distance between two successful crest

6 0
3 years ago
Read 2 more answers
In the waves lab you change blank to see how it would affect wave speed​
GaryK [48]

where is the question in this ????

7 0
3 years ago
B) What are the only two sources of energy that produce all the energy we use on Earth? What form
Zina [86]

Answer:

Solar and nuclear power generate more than 99 percent of our civilization's energy. Every other important source of energy is a combination of these two. The majority of them are solar in nature. We discharge previously collected solar energy when we burn wood.

and

Nuclear energy, fossil energy (oil, coal, and natural gas), and renewable energy (wind, solar, geothermal, and hydropower) are all examples of primary energy sources.

Explanation:

4 0
3 years ago
Heat flows into a gas in a piston and work is performed on the gas by its surroundings. The amount of work done is equal to the
inna [77]

Answer:

The Internal energy of the gas did not change

Explanation:

In this situation the Internal energy of the gas did not change and this is because according the the first law of thermodynamics

Δ U = Q - W  ------ ( 1 )

Δ U  = change in internal energy

Q = heat added

W = work done

since Q = W.  the value of ΔU  will be = zero   i.e. No change

4 0
3 years ago
Scientists hypothesize that there are no dinosaurs alive today because
Wittaler [7]
Its c after the meteorite hit earth it created a different environment worldwide that animals weren't able to adapt to due to its harsh conditions 
8 0
3 years ago
Read 2 more answers
Other questions:
  • A 30.0 kg cart travelling at 5.00 m/s collides with a 50.0 kg cart. Both carts immediately come to rest after the collision. Wha
    10·1 answer
  • I am getting tired quickly when I walk to school in the morning. What exercises can I do to help improve my level of fitness in
    8·2 answers
  • A substance contains only one type of atom. The substance is a/an ____________. A. solution B. element C. mixture D. compound
    14·2 answers
  • The longer the lever, the greater the
    14·1 answer
  • Asteroid Ida was photographed by the Galileo spacecraft in 1993, and the photograph revealed that the asteroid has a small moon,
    10·1 answer
  • B-1:
    8·1 answer
  • Which planet would float if placed in water
    8·1 answer
  • Let's say you cut open a log of wood with an axe, what type of simple machine are you using? Does it matter how sharp it is?
    14·2 answers
  • How many half-lives have passed if a sample contains 25% of its original carbon-14?
    7·1 answer
  • What is your ideal high school experience?
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!