HELP ME FOR NUMBER 1 THROUGH 4

A Juggler is juggling a uniform rod one end of which is coated in tar and burning. He is holding the rod by the opposite end and

lyudmila [28]

The vertical speed of the rod varies inversely as the rotational speed for a given number of complete rotations

The equation that gives the vertical velocity, v₀ is $\, \underline{v_0= \dfrac{ g \cdot \pi \cdot n}{ \omega_0 }}$

Reason:

From a similar question, the given parameters appear to be correctly given as follows;

The vertical speed of the rod = v₀

Angular velocity of the = ω₀

Required;

The value of, v₀, so that the rod has made exactly, n, number of turns when it returns to his hand

Where;

n = An integer

Solution;

The time the rod spends in the air is given as follows;

$Height, \ h = u \cdot t - \dfrac{1}{2} \cdot g \cdot t^2$

Where;

g = Acceleration due to gravity

t = Time of motion

When the rod returns to his hand, we have, h = 0, therefore;

$0 = u \cdot t - \dfrac{1}{2} \cdot g \cdot t^2$

$u \cdot t = \dfrac{1}{2} \cdot g \cdot t^2$

$t^2 = \dfrac{u \cdot t }{\dfrac{1}{2} \cdot g } = \dfrac{2 \cdot u \cdot t }{g }$

$Time, \ t = \dfrac{2 \cdot u }{g }$

We have;

$Angular \ velocity, \ \omega_0 = \dfrac{ 2 \cdot \pi \cdot n}{t} \ (required)$

$\omega_0 = \dfrac{ 2 \cdot \pi \cdot n}{ \dfrac{2 \cdot v_0 }{g }} = \dfrac{ g \cdot \pi \cdot n}{ v_0 }$

Therefore;

$The \ vertical \ velocity, \, \underline{v_0= \dfrac{ g \cdot \pi \cdot n}{ \omega_0 }}$

Learn more here:

brainly.com/question/14140053

4 0

3 years ago

Three individual point charges are placed at the following positions in the x-y plane:Q3= 5.0 nC at (x, y) = (0,0);Q2= -3.0 nC a

ozzi

Answer:

Explanation:

net force exerted on charge Q₃, exerted by charges Q₁and Q₂, will be zero

if net electric field due to charges Q₁ and Q₂ at origin is zero .

electric field due to Q₂

= 9 X 10⁹ X 3 x10⁹ / .04²

electric field due to Q₁

= 9 X 10⁹ X Q₁ / .02²

For equilibrium

9 X 10⁹ X Q₁ / .02² = 9 X 10⁹ X 3 x10⁻⁹ / .04²

Q₁ = 3 X10⁻⁹ x .02² / .04²

= 3 / 4 x 10⁻⁹

.75 x 10⁻⁹ C

8 0

3 years ago

Density is determined by:

Irina18 [472]

The mass of an object divided by its volume

3 0

3 years ago

Sophia is planning on going down an 8-m water slide. Her weight is 50 N. She knows that she has gravitational potential energy (

RideAnS [48]

Answer:

Explanation:

graph would be a straight line from (0, 0) to (400, 8)

Plot points are

PE = mgh

50(0) = 0 J

50(2) = 100 J

50(4) = 200 J

50(6) = 300 J

50(8) = 400 J

4 0

3 years ago

How does an object's position and velocity change as the object accelerates?”

taurus [48]

Answer:

aerodynamics

Explanation:

if an object like a car is going 200 mph at max speed and then the car gets aerodynamic or smoothed to the point that air can get by the car it could end up going another 20 mph faster

7 0

3 years ago