Answer:
A) 3.13 m/s
B) 5.34 N
C) W = 26.9 J
Explanation:
We are told that the position as a function of time is given by;
x(t) = αt² + βt³
Where;
α = 0.210 m/s² and β = 2.04×10^(−2) m/s³ = 0.0204 m/s³
Thus;
x(t) = 0.21t² + 0.0204t³
A) Velocity is gotten from the derivative of the displacement.
Thus;
v(t) = x'(t) = 2(0.21t) + 3(0.0204t²)
v(t) = 0.42t + 0.0612t²
v(4.5) = 0.42(4.5) + 0.0612(4.5)²
v(4.5) = 3.1293 m/s ≈ 3.13 m/s
B) acceleration is gotten from the derivative of the velocity
a(t) = v'(t) = 0.42 + 2(0.0612t)
a(4.5) = 0.42 + 2(0.0612 × 4.5)
a(4.5) = 0.9708 m/s²
Force = ma = 5.5 × 0.9708
F = 5.3394 N ≈ 5.34 N
C) Since no friction, work done is kinetic energy.
Thus;
W = ½mv²
W = ½ × 5.5 × 3.1293²
W = 26.9 J
The strength of the gravitational field is given by:

where
G is the gravitational constant
M is the Earth's mass
r is the distance measured from the centre of the planet.
In our problem, we are located at 300 km above the surface. Since the Earth radius is R=6370 km, the distance from the Earth's center is:

And now we can use the previous equation to calculate the field strength at that altitude:

And we can see this value is a bit less than the gravitational strength at the surface, which is

.
Answer:
Option 5.
Explanation:
Many of the properties of water like high specific heat, cohesion, high vaporization heat, etc can be contributed to the polar nature of water molecule.
Water being a polar molecule as it contains positively charged hydrogen and an electro-negative oxygen which results in uneven or non uniformity in sharing of electrons which leads to dipole formation and hence polarization of the molecule due to which it attracts its neighboring molecules.
This polar nature imparts the properties like cohesion, surface tension , adhesion, etc due to the presence of hydrogen bonds in water molecule.
Answer:
Momentum after collision will be 6000 kgm/sec
Explanation:
We have given mass of the whale = 1000
Initial velocity v = 6 m/sec
It collides with other mass of 200 kg which is at stationary
Initial momentum of the whale = 1000×6 = 6000 kgm/sec
We have to find the momentum after collision
From conservation of momentum
Initial momentum = final momentum
So final momentum = 6000 kgm/sec
<span>when it returns to its original level after encountering air resistance, its kinetic energy is
decreased.
In fact, part of the energy has been dissipated due to the air resistance.
The mechanical energy of the ball as it starts the motion is:
</span>

<span>where K is the kinetic energy, and where there is no potential energy since we use the initial height of the ball as reference level.
If there is no air resistance, this total energy is conserved, therefore when the ball returns to its original height, the kinetic energy will still be 100 J. However, because of the presence of the air resistance, the total mechanical energy is not conserved, and part of the total energy of the ball has been dissipated through the air. Therefore, when the ball returns to its original level, the kinetic energy will be less than 100 J.</span>