The magnitude of the net displacement is 95.3 m
Explanation:
To find the magnitude of the net displacement, we have to resolve each of the two displacements into the horizontal and vertical direction first.
1st displacement is:
at 
So its components are

2nd displacement is:
at 
So its components are

Therefore, the x- and y-components of the net displacement are:

Therefore, the magnitude of the final displacement is:

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Answer:
563.86 N
Explanation:
We know the buoyant force F = weight of air displaced by the balloon.
F = ρgV where ρ = density of air = 1.29 kg/m³, g = acceleration due to gravity = 9.8 m/s² and V = volume of balloon = 4πr/3 (since it is a sphere) where r = radius of balloon = 2.20 m
So, F = ρgV = ρg4πr³/3
substituting the values of the variables into the equation, we have
F = 1.29 kg/m³ × 9.8 m/s² × 4π × (2.20 m)³/3
= 1691.58 N/3
= 563.86 N
Answer:
1. t = 0.0819s
2. W = 0.25N
3. n = 36
4. y(x , t)= Acos[172x + 2730t]
Explanation:
1) The given equation is

The relationship between velocity and propagation constant is

v = 15.87m/s
Time taken, 

t = 0.0819s
2)
The velocity of transverse wave is given by


mass of string is calculated thus
mg = 0.0125N

m = 0.00128kg


0.25N
3)
The propagation constant k is

hence

0.036 m
No of wavelengths, n is

n = 36
4)
The equation of wave travelling down the string is
![y(x, t)=Acos[kx -wt]\\\\becomes\\\\y(x , t)= Acos[(172 rad.m)x + (2730 rad.s)t]](https://tex.z-dn.net/?f=y%28x%2C%20t%29%3DAcos%5Bkx%20-wt%5D%5C%5C%5C%5Cbecomes%5C%5C%5C%5Cy%28x%20%2C%20t%29%3D%20Acos%5B%28172%20rad.m%29x%20%2B%20%282730%20rad.s%29t%5D)
![without, unit\\\\y(x , t)= Acos[172x + 2730t]](https://tex.z-dn.net/?f=without%2C%20unit%5C%5C%5C%5Cy%28x%20%2C%20t%29%3D%20Acos%5B172x%20%2B%202730t%5D)
Answer: For ideal machine efficiency = 1. Hence M.A = V. R. The V. R of an ideal machine and the practical machine is a constant or is the same for both
Answer:
860.6 years.
Explanation:
The parameters given are;
Initial detector activity = 370000 alpha decays per second
Final detector activity = 93000 alpha decays per second
Formula for time to change in activity is given by the following relation;

t₉₃₀₀₀ = 2.72 × 10¹⁰ seconds = 860.6 years.