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
Kipish [7]
3 years ago
13

In a game of pool, the cue ball strikes another ball of the same mass and initially at rest. After the collision, the cue ball m

oves at 4.60 m/s along a line making an angle of 28.0° with its original direction of motion, and the second ball has a speed of 3.40 m/s. Find (a) the angle between the direction of motion of the second ball and the original direction of motion of the cue ball and (b) the original speed of the cue ball.
Physics
1 answer:
ikadub [295]3 years ago
7 0

(a) -39.4^{\circ}

Let's take the initial direction (before the collision) of the cue ball has positive x-direction.

Along the y-direction, the total initial momentum is zero:

p_y =0

Therefore, since the total momentum must be conserved, it must be zero also after the collision. So we write:

0 = m v_1 sin \phi_1 + m v_2 sin \phi_2 \\0 = m(4.60) sin (28^{\circ}) + m(3.40) sin \phi_2

where

m is the mass of each ball

v_1= 4.60 m/s is the velocity of the cue ball after the collision

v_2 = 3.40 m/s is the velocity of the second ball after the collision

\phi_1=28.0^{\circ} is the angle of the cue ball with the x-axis

\phi_2 is the angle of the second ball

Solving for \phi_2, we find the angle between the direction of motion of the second ball and the original direction of motion:

sin \phi_2 = -\frac{4.60 sin 28}{3.40}=-0.635\\\phi_2 = -39.4^{\circ}

(b) 6.69 m/s

To find the original speed of the cue ball, we analyze the situation along the horizontal direction.

First, we calculate the total momentum along the x-direction after the collision, which is:

p_x = m v_1 cos \phi_1 + m v_2 cos \phi_2 \\0 = m(4.60) cos (28^{\circ}) + m(3.40) cos (-39.4^{\circ})=6.69 m

The initial total momentum along the x-direction as

p_x = m u

where

m is the mass of the cue ball

u is the initial velocity of the cue ball

The momentum along this direction must be conserved, so we can equate the two expressions and find the value of u:

mu = 6.69 m\\u = 6.69 m/s

You might be interested in
Suppose that a planet were discovered between the sun and Mercury, with a circular orbit of radius equal to 2/3 of the average o
Musya8 [376]

Explanation:

It is given that,

A planet were discovered between the sun and Mercury, with a circular orbit of radius equal to 2/3 of the average orbit radius of Mercury.

Mass of the Sun, M=1.99\times 10^{30}\ kg

Radius of Mercury's orbit, r=5.79\times 10^{10}\ m

Radius of discovered planet, R=\dfrac{2}{3}r

R=\dfrac{2}{3}\times 5.79\times 10^{10}\ m=3.86\times 10^{10}\ m

Let T is the orbital period of such a planet. Using Kepler's third law of planetary motion as :

T^2\propto R^3

T^2=\dfrac{4\pi^2R^3}{GM}

T^2=\dfrac{4\pi^2\times (3.86\times 10^{10})^3}{6.67\times 10^{-11}\times 1.99\times 10^{30}}

T=\sqrt{1.71\times 10^{13}}

T = 4135214.625 s

or

T = 47.86 days

So, the orbital period of such a planet is 47.86 days. Hence, this is the required solution.

6 0
3 years ago
What two factors affect the strength of a magnetic field
Stels [109]

Answer:

Factors Affecting the Strength of the Magnetic Field of an Electromagnet: Factors that affect the strength of electromagnets are the nature of the core material, strength of the current passing through the core, the number of turns of wire on the core and the shape and size of the core.

Explanation:

I HOPE I HELPED :)

7 0
3 years ago
Jason knows that the equation to calculate the period of a simple pendium T=2π√L/8, where T is the period, L is the length of th
erik [133]

Answer: L can be expressed in terms of g and f as

L = g/(2πf)^2

Explanation: Please see the attachments below

3 0
3 years ago
On a very muddy football field, a 110kg linebacker tackles an 85kg halfback. Immediately before the collision, the linebacker is
Alchen [17]
<span>Using conservation of energy and momentum you can solve this question. M_l = mass of linebacker
M_ h = mass of halfback
V_l = velocity of linebacker
V_h = velocity of halfback

So for conservation of momentum,
rho = mv

M_l x V_li + M_h x V_hi = M_l x V_lf + M_h x V_hf

For conservation of energy (kinetic)
E_k = 1/2mv^2/ 1/2mV_li^2 + 1/2mV_{hi}^2 = 1/2mV_{lf}^2 + 1/2mV_{hf}^2

Where i and h stand for initial and final values.
We are already told the masses, \[M_l = 110kg\] \[M_h = 85kg\] and the final velocities \[V_{fi} = 8.5ms^{-1}\] and \[V_{ih} = 7.2ms^{-1} </span>
6 0
3 years ago
1. Earth releases about 44-46 Tw of heat, in fact heat can be converted into
Aleksandr [31]

Answer:

  even if it all could be used, it wouldn't be enough

Explanation:

The land area of the US is about 5.45% of the world's area, so the amount of released heat over the area of the US is on the order of 2.4 Tw. Current technology for converting geothermal energy to electricity is about 12% efficient, so the available energy might amount to 0.29 Tw if it could all be captured.

Energy consumption in the US in 2019 was on the order of 0.46 Tw. This suggests that even if <em>all</em> of the thermal energy radiated by the Earth from the US could be turned to useful forms of energy, it would meet only about 60% of the US need for energy.

8 0
3 years ago
Other questions:
  • Why are New Hampshire students required to learn about earths systems
    8·1 answer
  • a 645 N person is wearing stiletto shoes. If she lifts her left leg, and rocks back onto the heel under her right leg, the press
    14·1 answer
  • Maple syrup, which comes from the sap of maple trees, contains water and natural sugars. It's a clear, brown liquid and the suga
    11·1 answer
  • A ball rolls downhill with a constant acceleration of 4m/s squared. If it started from rest,it’s velocity at the end of 3 meters
    10·1 answer
  • A 6.53 !1014 Hz electromagnetic wave propagates in carbon tetrachloride with a speed of 2) 2.05 !108 m/s.
    15·1 answer
  • A loop of wire in the shape of a rectangle rotates with a frequency of 219 rotation per minute in an applied magnetic field of m
    6·1 answer
  • b. Comparing and Contrasting Compare the change in atmospheric pressure with elevation to the change in water pressure with dept
    5·1 answer
  • An object is dropped from a bridge. A second object is thrown downwards 1.0 s later. They both reach the water 20 m below at the
    12·1 answer
  • Num determinado equipamento industrial, um líquido de calor específico 0,50 cal/g.°C, entra a 20 °C e sai a 80 °C. Se a vazão de
    13·1 answer
  • A particle moves in a straight line with the velocity function v ( t ) = sin ( w t ) cos 3 ( w t ) . find its position function
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!