We have to add two vectors.
Vector #1: 0.15 m/s north
Vector #2: 1.50 m/s east
Their sum:
Magnitude: √(0.15² + 1.50²)
Magnitude = √(0.0225+2.25)
Magnitude = √2.2725
Magnitude = <em>1.5075 m/s</em>
Direction = arctan(0.15/1.50) north of east
Direction = <em>5.71° north of east</em>
Ok, assuming "mj" in the question is Megajoules MJ) you need a total amount of rotational kinetic energy in the fly wheel at the beginning of the trip that equals
(2.4e6 J/km)x(300 km)=7.2e8 J
The expression for rotational kinetic energy is
E = (1/2)Iω²
where I is the moment of inertia of the fly wheel and ω is the angular velocity.
So this comes down to finding the value of I that gives the required energy. We know the mass is 101kg. The formula for a solid cylinder's moment of inertia is
I = (1/2)mR²
We want (1/2)Iω² = 7.2e8 J and we know ω is limited to 470 revs/sec. However, ω must be in radians per second so multiply it by 2π to get
ω = 2953.1 rad/s
Now let's use this to solve the energy equation, E = (1/2)Iω², for I:
I = 2(7.2e8 J)/(2953.1 rad/s)² = 165.12 kg·m²
Now find the radius R,
165.12 kg·m² = (1/2)(101)R²,
√(2·165/101) = 1.807m
R = 1.807m
Answer:
Explanation:
wave length of light λ = 623 x 10⁻⁹ m .
Distance of screen D = 76.5 x 10⁻² m
width of slit = d
Distance on the screen between the second order minimum and the central maximum = 2 λ D / d
1.11 x 10⁻² = (2 x 623 x 10⁻⁹ x 76.5 x 10⁻² )/ d
d = ( 2 x 623 x 10⁻⁹ x 76.5 x 10⁻²) / 1.11 x 10⁻²
= 85872.97 x 10⁻⁹
= 85.87297 x 10⁻⁶
= 85.87 μm
width a of the slit is = 85.87 μm
