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
melomori [17]
3 years ago
6

For a given velocity of projection in a projectile motion, the maximum horizontal distance is possible only at ө = 45°. Substant

iate your answer with mathematical support.
Physics
1 answer:
myrzilka [38]3 years ago
6 0

First let us imagine the projectile launched at initial velocity V and at angle θ relative to the horizontal. (ignore wind resistance)

Vertical component y:

The initial vertical velocity is given as Vsinθ
The moment the projectile reaches the maximum height of h, the vertical velocity will be 0, therefore the time t taken to attain this maximum height is:

h = Vsinθ - gt
0 = Vsinθ - gt
t = (Vsinθ)/g

where g is  acceleration due to gravity

Horizontal component x:
The initial horizontal velocity is given as Vcosθ. However unlike the vertical component, this horizontal velocity remains constant because this is unaffected by gravity. The time to travel the horizontal distance D is twice the value of t times the horizontal velocity.
D = Vcosθ*[(2Vsinθ)/g] 
D = (2V²sinθ cosθ)/g 
 D = (V²sin2θ)/g

In order for D (horizontal distance) to be maximum, dD/dθ = 0
That is,

2V^2 cos2θ / g = 0
And since 2V^2/g must not be equal to zero, therefore cos(2θ) = 0
This is true when 2θ = π/2  or  θ = π/4


Therefore it is now<span> shown that the maximum horizontal travelled is attained when the launch angle is π/4 radians, or 45°.</span>

You might be interested in
Which EOC organizational structure is familiar and aligns with the on-scene incident organization?
dimulka [17.4K]

Answer:

Incident Command Structure, ICS or ICS-like EOC Structure is familiar and aligns with the on-scene incident organization. ICS or ICS-like EOC Structure is familiar and aligns with the on-scene incident organization.

3 0
3 years ago
How does kinetic energy affect the stopping distance of small vehicle compared to a large vehicle
Nadusha1986 [10]
The kinetic energy for a large vehicle is different from that of a smaller vehicle, assuming that the vehicles are travelling at the same speed and stopping the same distance. This is because for a larger vehicle the kinetic energy is higher, as the mass for a larger vehicle, is more than the smaller vehicle.
4 0
3 years ago
A car has a mass of 1.00 × 103 kilograms, and it has an acceleration of 4.5 meters/second2. What is the net force on the car
Novay_Z [31]

Answer:

4.5 *10^{3}\ kgm/s^{2}

Explanation:

Given:

Mass= 1.00 * 10^{3} \ kilograms,\\Acceleration =4.5\  meters/second^{2}

As we know that

Force=Mass * Acceleration

Putting the value of mass and Acceleration  we get ,

Force\  = \ 1.00 * 10^{3} * 4.5\ m/s^{2}

Force\  =4.5 * \ 10^{3} \  kgm/s^{2}

Therefore Net force is :4.5 *10^{3}\ kgm/s^{2}

0 0
2 years ago
Please help me find the answer for #2
Anit [1.1K]
D. a train on a straight track
6 0
3 years ago
Oil flows upward in the wick of a lantern because of liquid property called
nordsb [41]
Capillarity "Capillarity causes the part of the surface of a liquid in contact with a solid, to be either elevated above (e.g. water), or depressed below (e.g. mercury), the rest of the surface. This trait is named for the behaviour of liquids in capillary tubes placed perpendicular to the surface. The forces operating within capillarity are cohesion, adhesion, and surface tension."



6 0
2 years ago
Other questions:
  • Suppose that an asteroid traveling straight toward the center of the earth were to collide with our planet at the equator and bu
    9·1 answer
  • A wire 50 cm long with an east-west orientation carries a current of 7.0 A eastward. There is a uniform magnetic field perpendic
    6·2 answers
  • An airplane pilot sets a compass course due west and maintains a speed of 220 km/h. after flying for a half hour she finds herse
    5·2 answers
  • The electromagnetic spectrum is composed of many colors that possess different wavelengths. Which color possesses the shortest?
    7·1 answer
  • SECTION B<br>THEORY QUESTIONS<br>(1a) Define the following<br>(a) Work:​
    6·1 answer
  • Javier wants to improve his flexibility and increase his personal discipline. Which community resource should he select?
    11·1 answer
  • A small rubber ball is launched by a compressed-air cannon from ground level with an initial speed of 11.8 m/s directly upward.
    15·1 answer
  • A stone tumbles into a mine shaft strikes bottom after falling for 3.8 seconds. How deep is the mine shaft
    11·1 answer
  • Nine steps for developing scientific principles are
    9·1 answer
  • Which of the following is NOT considered electromagnetic radiation? x-rays radio waves cosmic rays ultraviolet light
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!