Answer:
A) 29.4 m 17.0 m; B) 2 m
Explanation:
If a vector is 34.0 m in length and is directed 60.0° east of north (which means 30.0° over the horizontal), then its coordinates will be:
Horizontal: (34.0 m)cos(30.0°)=29.4 m
Vertical: (34.0 m)sin(30.0°)=17 m
If one person walks 8.0 meters in a straight line and then walks 5.0 meters in another straight line, then the minimum displacement would be to go back over his tracks, displacing himself 8m-5m=3m, while the maximum displacement would be going straight ahead, displacing himself 8m+5m=13m. Any answer outside this interval is impossible (2m).
The efficiency of a machine is the ratio between the output power and the power in input:

in our problem, the output power is 3760 W while the input power is 4000 W, so the efficiency is

So the efficiency of the machine is 94%.
Answer:
The value of the time constant is 558.11 sec.
Explanation:
Given that,
Pendulum length = 1 m
Initial angle = 15°
Time = 1000 s
Reduced amplitude = 2.5°
We need to calculate the value of the time constant
Using formula of damping oscillation

Where,
=amplitude
=amplitude at t = 0
Put the value into the formula





Hence, The value of the time constant is 558.11 sec.
Answer:
The object´s displacement vector is Δr = 8i - 6 j
Explanation:
Hi there!
The position vector is given by the following function:
r = t²i - (3t + 3) j
Let´s find the position of the object at time t1 and t2:
At t1 = 1 s:
r1 = (1)² i - (3 · (1) + 3 )j
r1 = 1 i - 6 j
At t2 = 3 s:
r2 = (3)² i - (3 · (3) + 3) j
r2 = 9 i - 12 j
The displacement is calculated as follows:
displacement = Δr = final position - initial position = r2 - r1
r2 - r1 = 9 i - 12 j - (1 i - 6 j)
r2 - r1 = 9 i - 12 j - 1 i + 6 j
r2 - r1 = 8 i - 6 j
The object´s displacement vector is Δr = 8i - 6 j