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
klasskru [66]
3 years ago
7

A father racing his son has 1/2 the kinetic energy of the son, who has 1/3 the mass of the father. The father speeds up by 1.4 m

/s and then has the same kinetic energy as the son. What are the original speeds of (a) the father and (b) the son?
Physics
2 answers:
BaLLatris [955]3 years ago
3 0

Answer: a) 0.78 m/s b) 1.57 m/s

Explanation:

M = father's mass


m = son's mass = M/3


V = father's initial speed


v = son's initial speed

(1/2)MV^2 = (1/2)*(1/2)*m v^2


M*V^2 = (1/2)(M/3)v^2


V^2/v^2 = 1/4


V = v/2

Second equation:


(1/2)M*(V + 1.4)^2 = (1/2)m*v^2


= (1/2)*(M/3)*(3V)^2


cancel out the M's and (1/2)'s


(V + 1.4)^2 = 3V^2


V^2 + 2.8V + 1.96 = 3V^2


V^2 -1.4V -0.98 = 0

V^2 = 0.98/0.4 = 2.45

V = 1.57

Viefleur [7K]3 years ago
3 0

Answer:

a) The speed of the father is 3.38 m/s

b) The speed of the son is 8.28 m/s

Explanation:

Hi there!

The equation of kinetic energy is as follows:

KE = 1/2 · m · v²

Where:

KE = kinetic energy

m = mass

v = speed

The kinetic energy of the father will be:

KEf = 1/2 · mf · vf²

Where the letter "f" indicates "father"

The kinetic energy of the son will be:

KEs = 1/2 · ms · vs²

KEs = 1/2 · (1/3 · mf) · vs²

Where the letter "s" indicates "son".

We know that the kinetic energy of the father is half the kinetic energy of the son. Then:

KEf = 1/2 KEs

1/2 · mf · vf² = 1/2 · (1/2 · 1/3 · mf · vs²)

Let´s solve this equation for vf:

1/2 · mf · vf² = 1/12 · mf · vs²

Multiply by 2 and divide by mf both sides of the equation:

vf² = 1/6 · vs²

6 · vf² = vs²

We also know that when the father speeds up by 1.4 m/s the kinetic energy of the son and father is equal. Then:

KEf = 1/2 · mf · (vf + 1.4 m/s)²

KEs = 1/2 · 1/3 · mf · vs²

KEf = KEs

1/2 · mf · (vf + 1.4 m/s)² =  1/2 · 1/3 · mf · vs²

divide both sides of the equation by mf and 1/2

(vf + 1.4 m/s)² = 1/3 · vs²

(vf + 1.4 m/s) · (vf + 1.4 m/s) = 1/3 · vs²

vf² +2.8 vf + 1.96 = 1/3 · vs²

Replace vs² by 6 vf²

vf² +2.8 vf + 1.96 = 1/3 · 6 vf²

vf² +2.8 vf + 1.96 = 2 vf²

subtract 2 vf to both sides of the equation:

-2 vf² + vf² +2.8 vf + 1.96 = 0

-1 vf² + 2.8 vf + 1.96 = 0

Let´s solve the quadratic equation using the quadratic formula:

a = -1

b = 2.8

c = 1.96

vf = [-b ± √(b² - 4ac)]/2a

vf = 3.38 m/s

(The other solution of the quadratic equation is negative and therefore discarded).

The speed of the son will be:

6 · vf² = vs²

6 · (3.38 m/s)² = vs²

vs = 8.28 m/s

Then, the velocity of the son is 8.28 m/s and the velocity of the father is 3.38 m/s

You might be interested in
Which of the following is not a greenhouse gas?
Harman [31]

Answer:

The answer is B

Explanation: Greenhouse gases must be able to change their vibrational state in order to absorb infrared radiation or heat. SO therefore helium is not one of them.

Hope this helps:)

6 0
2 years ago
Which of the following is not found in dry air?
tensa zangetsu [6.8K]
C.water vapor i hope i helped

5 0
3 years ago
When light falls on objects, it interacts with them in different ways as shown in the images. What type of interaction is seen i
agasfer [191]

Answers with explanation

1)

Transmission

If all the light passes through a medium without any absorption then transmittance is 100%.

2)

Refraction

Refraction is the bending of a wave when it enters a medium where its speed is different and rays are again refracted when they leave that medium,

3)

Reflection

Reflected rays don't pass through the medium instead rays bounces off an object at an angle.

7 0
3 years ago
calculate the displacement of a mouse walking along a ruler, if it begins at the location x=5cm, and then walks yo x=12cm
Ivan
The displacement will be 7 cm
7 0
3 years ago
What should you do after handling chemicals in the lab
Natalija [7]

Answer:

Wash your hands with warm water and soap.

6 0
3 years ago
Other questions:
  • Which is NOT a property of gold? Select one: a. rare b. malleable c. tarnishes d. corrosion resistant
    12·2 answers
  • how do you isolate t (time) in this equation? the question is asking me to derive an equation for time to hit the ground for a d
    13·1 answer
  • Which describes the two parts of a measurement? a unit and a symbol a conversion factor and a number a symbol and a conversion f
    11·2 answers
  • Which of the options is the best definition of a vector?
    15·1 answer
  • A bird is flying directly toward a stationary bird-watcher and emits a frequency of 1420 Hz. The bird-watcher, however, hears a
    14·1 answer
  • A uniform ladder stands on a rough floor and rests against a frictionless wall. Since the floor is rough, it exerts both a norma
    5·1 answer
  • A device that transforms stored chemical energy into electrical energy is a(n)
    8·2 answers
  • A net force of 10 N accelerates a mass of 5 kg with an acceleration of 2
    13·1 answer
  • Select the correct answer.
    14·2 answers
  • You have managed to get a vacation on the Moon where the gravitational field strength is 1.6 N/kg. Gleefully, you kick a ball of
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!