The radius of the circular motion at the given speed is 1.56 m.
The given parameters;
- <em>speed of the rock, v = 2.5 m/s</em>
- <em>acceleration of the rock, a = 4 m/s²</em>
<em />
The radius of the circular motion is calculated by using centripetal acceleration formula as follows;

Thus, the radius of the circular motion at the given speed is 1.56 m.
Learn more about centripetal acceleration here: brainly.com/question/79801
Answer: Option (c) is the correct answer.
Explanation:
When the child is tossed up into the air then she gains kinetic energy as the child has moved from its initial position.
It is given that mass is 20 kg, velocity is
, and height is 2 m.
Calculate the kinetic energy of child as follows.
kinetic energy = 
= 
= 
= 
Also, when child falls off the ground then she will have gravitational potential energy.
Calculate gravitational potential energy of child as follows.
Potential energy = m × g × h
= 
= 
To solve this problem it is necessary to apply the concepts related to Hooke's Law as well as Newton's second law.
By definition we know that Newton's second law is defined as

m = mass
a = Acceleration
By Hooke's law force is described as

Here,
k = Gravitational constant
x = Displacement
To develop this problem it is necessary to consider the two cases that give us concerning the elongation of the body.
The force to keep in balance must be preserved, so the force by the weight stipulated in Newton's second law and the force by Hooke's elongation are equal, so

So for state 1 we have that with 0.2kg there is an elongation of 9.5cm


For state 2 we have that with 1Kg there is an elongation of 12cm


We have two equations with two unknowns therefore solving for both,


In this way converting the units,


Therefore the spring constant is 313.6N/m
Answer:
a)
, b) 
Explanation:
a) The minimum coeffcient of friction is computed by the following expression derived from the Principle of Energy Conservation:




b) The speed of the block is determined by using the Principle of Energy Conservation:




The radius of the circular loop is:



Answer:
R = 3.88 m
Explanation:
As the Chinook salmon leaves the water till it gets back into the water it is performing a projectile motion with the following parameters:
V₀ = Launch Speed = 6.7 m/s
θ = Launch Angle = 29°
R= Range of Projectile= Horizontal Distance Covered by Chinook salmon= ?
The value of the range of a projectile is given by the following formula:
R = (V₀² Sin 2θ)/g
R = [(6.7 m/s)² Sin {(2)(29°)}/(9.8 m/s²)]
R = [(6.7 m/s)² Sin (58°)/(9.8 m/s²)]
<u>R = 3.88 m</u>