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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>

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An object undergoes two successive displacements:
Gre4nikov [31]

The magnitude of the net displacement is 95.3 m

Explanation:

To find the magnitude of the net displacement, we have to resolve each of the two displacements into the horizontal and vertical direction first.

1st displacement is:

d_1=79 m at 16.9^{\circ}

So its components are

d_{1x}=(79)(cos 16.9^{\circ})=75.6 m\\d_{1y}=(79)(sin 16.9^{\circ})=23.0 m

2nd displacement is:

d_2=16.7 m at 31.1^{\circ}

So its components are

d_{2x}=(16.7)(cos 31.1^{\circ})=14.3 m\\d_{2y}=(16.7)(sin 31.1^{\circ})=8.6 m

Therefore, the x- and y-components of the net displacement are:

d_x=d_{1x}+d_{2x}=75.6+14.3=89.9 m\\d_y=d_{1y}+d_{2y}=23.0+8.6=31.6 m

Therefore, the magnitude of the final displacement is:

d=\sqrt{d_x^2+d_y^2}=\sqrt{(89.9)^2+(31.6)^2}=95.3 m

Learn more about displacement:

brainly.com/question/3969582

#LearnwithBrainly

8 0
2 years ago
A very long train is rolling at 4 m/s along a straight track. An observer is standing on the ground very dangerously close to th
hichkok12 [17]

Answer:

A. \vec{r}=(6\frac{m}{s})t\ \ \hat{i}

B.  t = 50 s

Explanation:

A. The vectorial equation of the person who is getting closer to the other person is:

\vec{r}=\vec{v}t

r: position vector

v: speed vector = 6m/s i  (if you consider the motion as a horizontal motion)

Then, you replace and obtain:

\vec{r}=(6\frac{m}{s})t\ \ \hat{i}

B. The time is:

t=\frac{d}{v}

d: distance to the observer = 300m

v: speed of the person on the car = 6.00 m/s

t=\frac{300m}{6m/s}=50s

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3 years ago
Which of the following statements about X-rays and radio waves is not true? Which of the following statements about X-rays and r
Lapatulllka [165]

Answer:

X-rays travel through space faster than radio waves.

Explanation:

Electromagnetic waves consist of oscillations of the electric and the magnetic field in a plane perpendicular to the direction of motion the wave.

All electromagnetic waves travel in a vacuum always at the same speed, the speed of light, whose value is:

c=3.0\cdot 10^8 m/s

Electromagnetic waves are classified into 7 different types, according to their wavelength/frequency. From shortest to longest wavelength (and so, from highest to lowest frequency), we have:

Gamma rays

X rays

Ultraviolet

Visible light

Infrared radiation

Microwaves

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Now we can analyze the 4 statements:

X-rays and radio waves are both forms of light, or electromagnetic radiation --> TRUE. They are both types of electromagnetic waves.

X-rays have higher frequency than radio waves. --> TRUE, as we can see from the table above.

X-rays have shorter wavelengths than radio waves. --> TRUE, as we can see from the table above.

X-rays travel through space faster than radio waves. --> FALSE: all electromagnetic waves travel in space at the same speed, the speed of light.

8 0
2 years ago
A rock with a mass of 0.3 kg falls from the top of a cliff. If it takes the rock 2.5 s to reach the ground, what was the impulse
kaheart [24]
Impulse=force x time
force=mass x acceleration due to gravity
force=
300 \times 10 = 3000
impulse =3000 x 2.5= ( sorry i don't have a calculator right now so you must calculate this yourself)
I converted from kg to g because it is the standard.
Hope this helps you.
4 0
3 years ago
Damage to the ___________ will most likely cause a person to lose the ability to comprehend language. (2 points)
Marina86 [1]

Answer: Wernicke's Area

Explanation: Wernicke's area is the region of the brain responsible for language <em>interpretation</em>. Broca's area is associated with language <em>production.</em>

6 0
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