Answer:
Part a)

Part b)

Part c)

Part d)
from t = 0 to t = 4.9 s
so the reading of the scale will be same as that of weight of the block
Then its speed will reduce to zero in next 3.2 s
from t = 4.9 to t = 8.1 s
The reading of the scale will be less than the actual mass
Explanation:
Part a)
When elevator is ascending with constant speed then we will have



So it will read same as that of the mass

Part b)
When elevator is decending with constant speed then we will have



So it will read same as that of the mass

Part c)
When elevator is ascending with constant speed 39 m/s and acceleration 10 m/s/s then we will have



Reading is given as



Part d)
Here the speed of the elevator is constant initially
from t = 0 to t = 4.9 s
so the reading of the scale will be same as that of weight of the block
Then its speed will reduce to zero in next 3.2 s
from t = 4.9 to t = 8.1 s
The reading of the scale will be less than the actual mass
Yes, all of these could be applied to a roller coaster.
Answer:
The tangential speed of the tack is 8.19 m/s.
Explanation:
The wheel rotates 3.37 times a second that means wheel complete 3.37 revolutions in a second. Therefore, the angular speed ω of the wheel is given as follows:

Use the relation of angular speed with tangential speed to find the tangential speed of the tack.
The tangential speed v of the tack is given by following expression
v = ω r
Here, r is the distance to the tack from axis of rotation.
Substitute 21.174 rad/s for ω, and 0.387 m for r in the above equation to solve for v.
v = 21.174 × 0.387
v = 8.19m/s
Thus, The tangential speed of the tack is 8.19 m/s.
Given,
A player kicks a soccer hits at an angle of 30° at a speed of 26 m/s
We can resolute the trajectory of soccer into horizontal and vertical components.(Please see the attached file)
We can have,
Horizontal velocity component of ball= 26cos(30°) = 26×(√3÷2) = 22.51 m/s
And vertical velocity component of ball = 26sin(26°) = 26×(1÷2) = 13 m/s