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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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2 years ago
Sunburn is caused by ultraviolet light waves having a frequency of around 10^16 Hz. What is their wavelength if the speed of lig
Taya2010 [7]

Given:\\f=10^{16}Hz\\c=3\cdot 10^8\frac{m}{s} \\\\Find:\\\lambda =?\\\\Solution:\\\\\lambda = \frac{c}{f} \\\\\lambda= \frac{3\cdot 10^8\frac{m}{s}}{10^{16}Hz} =3\cdot 10^{-8}m = 30nm

5 0
3 years ago
What is the answer to this question
Studentka2010 [4]

Answer:

0.11 m/s

Explanation:

From the question given above, the following data were obtained:

Initial displacement (d1) = 1.09 m

Final displacement (d2) = 2.55 m

Time (t) = 12.8 s

Average velocity =?

Next, we shall determine the total displacement (i.e change in displacement). This can be obtained as follow:

Initial displacement (d1) = 1.09 m

Final displacement (d2) = 2.55 m

Total displacement = d2 – d1

Total displacement = 2.55 – 1.09

Total displacement = 1.46 m

Finally, we shall determine the average velocity of the beetle. This can be obtained as follow:

Total Displacement = 1.46 m

Total time (t) = 12.8 s

Average velocity =?

Average velocity = Total Displacement / Total time

Average velocity = 1.46/12.8

Average velocity = 0.11 m/s

Thus, the average velocity of the beetle is 0.11 m/s

6 0
3 years ago
When a golfer tees off, the head of her golf club, which has a mass of 160 g, is traveling 50 m/s just before it strikes a 46 g
olya-2409 [2.1K]

Answer:

v1=21.81m/s

Explanation:

<em>When a golfer tees off, the head of her golf club, which has a mass of 160 g, is traveling 50 m/s just before it strikes a 46 g golf ball at rest on a tee. Immediately after the collision, the club head continues to travel in the same direction but at a reduced speed of 44 m/s. Neglect the mass of the club handle and determine the speed (in m/s) of the golf ball just after impact.</em>

According to the law of conservation of momentum, if the net external force on a system is zero, then the linear momentum of the system is conserved.

During collision of two particles, the external force on the system of two colliding particles is zero (only internal force acts between the colliding particles), therefore, the momentum is conserved during the collision.

Answer and Explanation:

Given :

head of the golf club=160g

velocity of the golf club=50 m/s

golf ball mass=46g

velocity=om/s

m1u1+m2u2=m1v1+m2v2.........................................1

160*50 +46*0=160*44+46*v1

8000=7040+46v1

960=46v1

v1=960/46

v1=21.81m/s

3 0
3 years ago
A straight 2.20 m wire carries a typical household current of 1.50 A (in one direction) at a location where the earth's magnetic
Y_Kistochka [10]

A) Upward

In order to find the direction of the magnetic force on the wire, we can use the right-hand rule: the index finger, the middle finger and the thumb of the right hand must be placed all of them perpendicular to each other.

So we have:

- Index finger: direction of current in the wire (from west to east)

- Middle finger: direction of magnetic field (from south to north)

- Thumb: direction of the force --> so it will be upward

So, the force will point upward.

B) 1.82\cdot 10^{-4}N

The magnitude of the force exerted by the magnetic field on the wire is given by

F=ILB

where

I = 1.50 A is the current in the wire

L = 2.20 m is the length of the wire

B=0.550 G = 0.55 \cdot 10^{-4}T

Substituting into the equation, we find

F=(1.50 A)(2.20 m)(0.55 \cdot 10^{-4} T)=1.82\cdot 10^{-4}N

7 0
3 years ago
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