Explanation:
The object is moving along the parabola y = x² and is at the point (√2, 2). Because the object is changing directions, it has a centripetal acceleration towards the center of the circle of curvature.
First, we need to find the radius of curvature. This is given by the equation:
R = [1 + (y')²]^(³/₂) / |y"|
y' = 2x and y" = 2:
R = [1 + (2x)²]^(³/₂) / |2|
R = (1 + 4x²)^(³/₂) / 2
At x = √2:
R = (1 + 4(√2)²)^(³/₂) / 2
R = (9)^(³/₂) / 2
R = 27 / 2
R = 13.5
So the centripetal force is:
F = m v² / r
F = m (5)² / 13.5
F = 1.85 m
The answer of this question is B.
Answer:
This is known as a Galilean transformation where
V' = V - U
Where the primed frame is the Earth frame and the unprimed frame is the frame moving with respect to the moving frame
V - speed of object in the unprimed frame
U - speed of primed frame with respect to the unprimed frame
Here we have:
V = -15 m/s speed of ball in the moving frame (the truck)
U = -20 m/s speed of primed (rest) frame with respect to moving frame
So V' = -15 - (-20) = 5 m/s
It may help if you draw a vector representing the moving frame and then add
a vector representing the speed of the ball in the moving frame.
First we need to find the acceleration of the skier on the rough patch of snow.
We are only concerned with the horizontal direction, since the skier is moving in this direction, so we can neglect forces that do not act in this direction. So we have only one horizontal force acting on the skier: the frictional force,

. For Newton's second law, the resultant of the forces acting on the skier must be equal to ma (mass per acceleration), so we can write:

Where the negative sign is due to the fact the friction is directed against the motion of the skier.
Simplifying and solving, we find the value of the acceleration:

Now we can use the following relationship to find the distance covered by the skier before stopping, S:

where

is the final speed of the skier and

is the initial speed. Substituting numbers, we find: