Answer:
D
Explanation:
When the sound is moving away from the stationary object the pitch decreases according to the Doppler Effect.
Answer with Explanation:
We are given that
Mass of adult,M=75 kg
Length of board=l=9 m
Mass of child=m=25 kg
a.Let pivot placed at point O so that the board is balanced ignoring the board's mass
Moment about the point O
![75x=25(9-x)](https://tex.z-dn.net/?f=75x%3D25%289-x%29)
![75x=225-25x](https://tex.z-dn.net/?f=75x%3D225-25x)
![75x+25x=225](https://tex.z-dn.net/?f=75x%2B25x%3D225)
![100x=225](https://tex.z-dn.net/?f=100x%3D225)
![x=\frac{225}{100}=2.25 m](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B225%7D%7B100%7D%3D2.25%20m)
Hence, the pivot placed at 2.25 m from the adult.
b.Mass of board=m''=15 kg
Center of board=![\frac{9}{2}=4.5 m](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B2%7D%3D4.5%20m)
Moment about point O
![75x=15(4.5-x)+25(4.5+(4.5-x))](https://tex.z-dn.net/?f=75x%3D15%284.5-x%29%2B25%284.5%2B%284.5-x%29%29)
![75x=67.5-15x+225-25x](https://tex.z-dn.net/?f=75x%3D67.5-15x%2B225-25x)
![75x+25x+15=67.5+225](https://tex.z-dn.net/?f=75x%2B25x%2B15%3D67.5%2B225)
![115x=292.5](https://tex.z-dn.net/?f=115x%3D292.5)
![x=\frac{292.5}{115}=2.5 m](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B292.5%7D%7B115%7D%3D2.5%20m)
Hence, the pivot point is 2.5 m from the adult.
Answer:
(a) Position Vectors V₁= -2î km, V₂=5î km
(b) Displacement Δx=7 km
Explanation:
Given data
Distance=2 km west at t=0
Distance=5 km east at t=6 min
Positive x is the east direction
To find
(a)Car position vector at given times
(b)Displacement between 0 to 6.0 min
Solution
For Part (a) car position vector at given times
At t=0 the distance=2 km west so conclude that x₁=-2 because it is in negative side So vector V₁
V₁= -2î km
At t=6.0 the distance=5 km east so conclude that x₂=5 because it is in positive side So vector V₂
V₂=5î km
For (b) displacement between 0 to 6.0 min
According to following mathematical law we can conclude that
Δx=x₂-x₁
Δx=5-(-2)km
Δx=7 km
Answer:
Total work done = 15,306.25 lb.ft
Explanation:
First of all, we know that;
Work done = Force x Distance.
Thus,
Work done to pull bucket (Wb) = 500 x 30 = 15,000 lb.ft
Now, work done by pulling the rope is given as a function of the length of the rope. Thus;
Wr =(x,x=0∫) F(x) dx
=(35,0∫) 0.5x dx
= 0.5[x²/2](35,0)
Thus,Wr = 0.5[(35²/2) - (0²/2)] = 0.5[612.5] = 306.25 lb.ft
Total work done will be the sum of that done to pull the bucket and that done to pull the rope.
Thus, Wt = Wb + Wr
Wt = 15000 + 306.25 = 15,306.25 lb.ft