Answer:
The translational kinetic energy is 225 J
The rotational kinetic energy is 225 J
Explanation:
Given;
mass of the wheel, m = 2-kg
linear speed of the wheel, v = 15 m/s
Transnational kinetic energy is calculated as;
E = ¹/₂MV²
where;
M is mass of the moving object
V is the velocity of the object
E = ¹/₂ x 2 x (15)²
E = 225 J
Rotational kinetic energy is calculated as;
E = ¹/₂Iω²
where;
I is moment of inertia
ω is angular velocity

E = ¹/₂ x 2 x (15)²
E = 225 J
Thus, the translational kinetic energy is equal to rotational kinetic energy
Explanation:
Problem 1.
Initial speed of the runner, u = 0
Acceleration of the runner, 
Time taken, t = 100 s
Let v is the speed of the runner now. Using the first equation of kinematics as :



v = 420 m/s
Problem 2.
Initial speed of the plane, u = 0
Distance covered, d = 300 m
Time taken, t = 25 s
Using the equation of kinematics as :





Problem 3.
A ball free falls from the top of the roof for 5 seconds. Let it will fall at a distance of d. It is given by :


d = 122.5 meters
Let v is the final speed at the end of 5 seconds. Again using first equation of kinematics as :


v = 49 m/s
Hence, this is the required solution.
2 meters per second for 8 seconds
1.5 meters per second for 8 seconds
The average speed should be 1.8 or 1.7 but I think its 1.8
a. 1.51 s
In this part of the problem, we are only interested in the horizontal motion of the ball. Along the horizontal direction, the motion of the ball is a uniform motion with constant velocity, which is equal to the horizontal component of the initial velocity:

So, the ball travels horizontally at a speed of 14.6 m/s; in order to cover the distance of d = 22.0 m that separates it from the wall, the time need is

b. 7.25 m
We now know that the ball takes 1.51 s to hit the wall, 22.0 away. Now we have to analyze the vertical motion of the ball, which is an accelerated motion with constant acceleration g =9.8 m/s^2 towards the ground (acceleration due to gravity).
The initial vertical velocity is

The vertical position of the ball at time t is given by the equation

We know that the ball hits the wall at t=1.51 s, so if we substitute this value into the previous formula, we find at what height y the ball hits the wall:
