Let the sphere is having charge Q and radius R
Now if the proton is released from rest
By energy conservation we can say
now take square root of both sides
so the proton will move by above speed and
here Q = charge on the sphere
R = radius of sphere
Answer:
v₀ₓ = 63.5 m/s
v₀y = 54.2 m/s
Explanation:
First we find the net launch velocity of projectile. For that purpose, we use the formula of kinetic energy:
K.E = (0.5)(mv₀²)
where,
K.E = initial kinetic energy of projectile = 1430 J
m = mass of projectile = 0.41 kg
v₀ = launch velocity of projectile = ?
Therefore,
1430 J = (0.5)(0.41)v₀²
v₀ = √(6975.6 m²/s²)
v₀ = 83.5 m/s
Now, we find the launching angle, by using formula for maximum height of projectile:
h = v₀² Sin²θ/2g
where,
h = height of projectile = 150 m
g = 9.8 m/s²
θ = launch angle
Therefore,
150 m = (83.5 m/s)²Sin²θ/(2)(9.8 m/s²)
Sin θ = √(0.4216)
θ = Sin⁻¹ (0.6493)
θ = 40.5°
Now, we find the components of launch velocity:
x- component = v₀ₓ = v₀Cosθ = (83.5 m/s) Cos(40.5°)
<u>v₀ₓ = 63.5 m/s</u>
y- component = v₀y = v₀Sinθ = (83.5 m/s) Sin(40.5°)
<u>v₀y = 54.2 m/s</u>
We have vector 
Therefore,
x component = 17.9 * cos80 degree = 3.108
y component = 17.9 * sin80 degrees = 17.628
<h3>What is a vector?</h3>
An object with both magnitude and direction is referred to be a vector. A vector can be visualized geometrically as a directed line segment, with an arrow pointing in the direction and a length equal to the magnitude of the vector. The vector points in a direction from its tail to its head.
If the magnitude and direction of two vectors match, they are the same vector. This shows that if we move a vector to a different location without rotating it, the final vector will be the same as the initial vector. The vectors that denote force and velocity are two examples. The direction of force and velocity are both fixed. The size of the vector would represent the force's strength or the velocity's corresponding speed.
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The attribute of any rotating object determined by the product of the moment of inertia and the angular velocity is known as angular momentum.
<h3>What is Angular Momentum?</h3>
- Without a kickstand, attempting to balance while getting on a bicycle will definitely result in you falling off. However, these wheels gain angular momentum once you begin pedaling. They're going to be resistant to change, which will make balance simpler.
- The definition of angular momentum is: any rotating object's characteristic determined by moment of inertia times angular velocity.
- It is a characteristic of rotating bodies determined by the sum of their moment of inertia and angular velocity. Since it is a vector quantity, the direction must also be taken into account in addition to the magnitude.
- Angular Momentum Examples : We encounter this property frequently, whether knowingly or unknowingly.
- The following provides some examples : Ice-skater
- In order to begin a spin, an ice skater starts with her hands and legs spread widely from the center of her body. She moves her hands and leg closer to her body when she needs to spin with more angular velocity, though.
- As a result, she conserves angular momentum and spins faster.
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B. Mining in the Guinean Forests of West Africa to provide diamond and gold jewelry for humans.
