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
Volgvan
3 years ago
5

A 3.9 g dart is fired into a block of wood with a mass of 24.6 g. The wood block is initially at rest on a 1.5 m tall post. Afte

r the collision, the wood block and dart land 3.5 m from the base of the post. Find the initial speed of the dart.
Physics
1 answer:
Galina-37 [17]3 years ago
4 0

Answer:

46.48m/s

Explanation:

The problem is a combination of the principle of conservation of linear momentum and projectile motion.

The principle of conservation of linear momentum states that in a closed system, the total momentum of colliding bodies before impact is equal to the total momentum after impact. The masses stated in the problem experienced an inelastic collision. In an inelastic collision, the bodies involved stick together after the collision and move with a common velocity.

For two bodies of masses m_1 and m_2 moving with velocities u_1 and u_2 before impact, if they experience inelastic collision, the conservation of their momenta is as stated in equation (1);

m_1u_1+m_2u_2=(m_1+m_2)v..................(1)

were v is their common velocity after impact. If the second mass m_2 was at rest before the impact, then its initial velocity u_2=0m/s. therefore m_2u_2=0. Equation (1) then becomes;

m_1u_1=(m_1+m_2)v..............(2)

In the problem stated, the second mass taken as the mass of the wooden block was at rest before the impact and the collision was inelastic since both the wood and the dart stuck together and moved with a common velocity after the impact. Therefore we can use equation (2) for the problem.

Given;

m_1=3.9g=0.0039kg\\u_1=?\\m_2=24.6g=0.0246kg\\v=?

Substituting these values into (2), we get the following;

0.0039*u_1=(0.0039+0.024)v\\0.0039u_1=0.0285v.........(3)

Their common v velocity after impact now makes both the wooden block and the dart (as a single body) to fall vertically through a height h of 1.5m over a range R of 3.5m as stated by the problem; hence by the principle of projectile motion for a body projected horizontally, the following relationship holds;

R= vt............(4)

were t is the time taken to fall through the height h. To obtain t we use the second equation of free fall under gravity;

h=\frac{1}{2}gt^2...........(5)

were g is acceleration due to gravity taken as 9.8m/s^2. Therefore;

1.5=\frac{1}{2}*9.8*t^2\\1.5=4.9t^2\\t^2=\frac{1.5}{4.9}=0.306\\t=\sqrt{0.306} =0.55s

We then substitute R and t into equation (4) to obtain v.

3.5=v*0.55\\v=\frac{3.5}{0.55}\\v=6.36m/s

We now further substitute this value of v into (3) to obtain u_1;

u_1=\frac{0.0285v}{0.0039}\\\\u_1=\frac{0.0285*6.36}{0.0039}\\\\u_1=\frac{0.18126}{0.0039}\\\\u_1=46.48m/s

You might be interested in
Why does water frozen in the cracks of a rock help to break down the rock? a) Water expands when frozen and chemically forces th
Gre4nikov [31]

Answer: B. water frozen in the cracks of a rock help to break down the rock because water expands when frozen, and physically forces the rock apart

6 0
3 years ago
Which is the best example of the concept of heredity? A. A black cat blends into its environment at night. B. A baby has his mot
Hitman42 [59]
B) A baby has his mother's hair and eye color 
4 0
3 years ago
Read 2 more answers
On topographic maps, contour lines that are farther apart indicate what ?
gladu [14]

Answer:

if I am correct, they indicate less steep terrain. think of it as the steeper the terrain the closer together the lines would be. hope that makes sense for you guys.

4 0
2 years ago
A planet in elliptical orbit around a star moves from the point in its orbit furthest from the star (A) to the closest point (P)
Virty [35]

Answer:

Zero work done,since the body isn't acting against  or by gravity.

Explanation:

Gravitational force is usually  considered as work done against gravity (-ve) and work by gravity ( +ve ) and also When work isn't done by or against gravity work done in this case is zero.

Gravitational force can be define as that force that attracts a body to any other phyical body or system that have mass.

The planet been considered as our system in this case is assumed to have mass, and ought to demonstrate such properties associated with gravitational force in such system. Such properties include the return of every object been thrown up as a result of gravity acting downwards. The orbiting nature of object along an elliptical part when gravitational force isn't acting on the body and it is assumed to be zero.

6 0
3 years ago
Which two statements offer evidence that the clocks energy is conserved?
Natali [406]

Answer:

C is the best answer because we all know that clock is part of our daily lives but we don't know the about its background

3 0
3 years ago
Read 2 more answers
Other questions:
  • When something could pose a danger, this could be a...
    13·2 answers
  • A sound wave traveling downward with a speed of about 4,000 m/s suddenly slows to 1,500 m/s not far below the Earth’s surface. W
    11·1 answer
  • Which condition describes an object having terminal velocity?
    8·2 answers
  • a scientist is creating a new synthetic material. the material’s density is 6.1 g/cm3. which sentences describe how the scientis
    14·2 answers
  • An incident ray parallel to the axis and one through the focal point reflect and converge at the image.
    7·2 answers
  • First to answer will be the brainliest I need the answer ASAP don't answer if you don't know the answer
    10·2 answers
  • Coherent light with wavelength 460 nm falls on a pair of slits. On a screen 1.86 m away, the distance between dark fringes is 3.
    6·1 answer
  • Mitchell records the amount of time a toy car takes to travel down a ramp one time for each of four slope angles. His lab
    8·1 answer
  • What is the force of an object that has a mass of 42 kg and an acceleration of 3 m/s22?
    13·1 answer
  • Jane, looking for Tarzan, is running at top speed (6.0 m/s ) and grabs a vine hanging vertically from a tall tree in the jungle.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!