Answer:
a.3.29 m/s
b.3.3 m/s
c.14.8 m
d.15 m
Explanation:
We have the following specifics:
Initial Horizontal speed=
Vertical component of initial speed=
Vertical distance=
a.
Applying the formula and considering g as negative results in 




b.Since the hundredths place exceeds 5, 1 is added to the tenths place, while other digits to the left remain unchanged and the digit to the right is replaced by 0.

c.Horizontal acceleration=

d.The digit in the tenths place at 8 surpasses 5, thus adding 1 to the units place, with all other digits on the left side unchanged and the right-side digit altered to 0.
Horizontal distance=15 m
Explanation:
Please refer to the attachment for the solution.
Answer:
The rotational angular speed is measured at 1.34 rad/s.
Explanation:
Considering the following parameters,
Length = 3.40 m
Distance = 5.90 m
Angle = 45.0°
We are tasked with finding the angular speed of rotation
Using the balance equation
Horizontal component


Vertical component

Substituting the tension value


Substituting the value into the equation


Thus, the angular speed of rotation computes to 1.34 rad/s.
Response:
0.60 m/s
Details:
The average speed between times t = a and t = b can be expressed as:
v_avg = (x(b) − x(a)) / (b − a)
Given the function x(t) = 0.36t² − 1.20t, and considering the interval from 1.0 to 4.0:
v_avg = (x(4.0) − x(1.0)) / (4.0 − 1.0)
v_avg = [(0.36(4.0)² − 1.20(4.0)) − (0.36(1.0)² − 1.20(1.0))] / 3.0
v_avg = [(5.76 − 4.8) − (0.36 − 1.20)] / 3.0
v_avg = [0.96 − (-0.84)] / 3.0
v_avg = 0.60
The average speed calculated is 0.60 m/s.