Answer:
(a)
(b) Kinetic Energy of planet with mass m₁, is KE₁ = 1.068×10³² J
Kinetic Energy of planet with mass m₂, KE₂ = 2.6696×10³¹ J
Explanation:
Here we have when their distance is d apart
Energy is given by
Conservation of linear momentum gives
m₁·v₁ = m₂·v₂
From which
v₂ = m₁·v₁/m₂
At equilibrium, we have;
which gives
multiplying both sides by m₂/m₁, we have
Such that v₁ =
Similarly, with v₁ = m₂·v₂/m₁, we have
From which we have;
and
The relative velocity = v₁ + v₂ =
v₁ + v₂ =
(b) The kinetic energy KE =
Just before they collide, d = r₁ + r₂ = 3×10⁶+5×10⁶ = 8×10⁶ m
= 10333.696 m/s
=2583.424 m/s
KE₁ = 0.5×2.0×10²⁴× 10333.696² = 1.068×10³² J
KE₂ = 0.5×8.0×10²⁴× 2583.424² = 2.6696×10³¹ J.
Given; Mass m = 65.0 Kg; acceleration a = 1.25 m/s²
Required: Force F = ?
Formula: F =ma
F = (65.0 Kg)(1.25 m/s²)
F = 81.25 N
Setting up an integral of
rotation is used as a method of of calculating the volume of a 3D object formed
by a rotated area of a 2D space. Finding the volume is similar to finding the
area, but there is one additional component of rotating the area around a line
of symmetry.
<span>First the solid of revolution
should be defined. The general function
is y=f(x), on an interval [a,b].</span>
Then the curve is rotated
about a given axis to get the surface of the solid of revolution. That is the
integral of the function.
<span>It all depends of the
function f(x), which must be known in order to calculate the integral.</span>
Answer:
A body is said to be moving with uniform speed, if it covers equal distances in equal intervals of time. ...