Answer:
a) 31.4 m/s
b) 50.2 m
Explanation:
a) When an object is free falling, its speed is determined by the gravity force giving it acceleration. Equation for the velocity of free fall started from the rest is:
v = g • t
g - is gravitational acceleration which is 9.81 m/s^2, sometimes rounded to 10
t - is the time of free fall
So:
v = 9.81 m/s^2 • 3.2
v = 31.4 m/s ( if g is rounded to 10, then the velocity is 10 • 3.2 = 32 m/s)
b) To determine the distance crossed in free fall we use the equation:
s = v0 + gt^2/2
v0 - is the starting velocity (since object started fall from rest, its v0 is 0)
s = gt^2/2
s = 9.81 m/s^2 • 3.2^2 / 2
s = 50.2 m (if we round g to 10 then the distance is 10 • 3.2^2/2 = 51.2 meters)
Answer:
r = 2.031 x 10⁶ m = 2031 km
Explanation:
In order for the asteroid to orbit the planet, the centripetal force must be equal to the gravitational force between asteroid and planet:
Centripetal Force = Gravitational Force
mv²/r = GmM/r²
v² = GM/r
r = GM/v²
where,
r = radial distance = ?
G = Universal Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²
M = Mass of Planet = 3.52 x 10¹³ kg
v = tangential speed = 0.034 m/s
Therefore,
r = (6.67 x 10⁻¹¹ N.m²/kg²)(3.52 x 10¹³ kg)/(0.034 m/s)²
<u>r = 2.031 x 10⁶ m = 2031 km</u>
1) 0.0011 rad/s
2) 7667 m/s
Explanation:
1)
The angular velocity of an object in circular motion is equal to the rate of change of its angular position. Mathematically:
where
is the angular displacement of the object
t is the time elapsed
is the angular velocity
In this problem, the Hubble telescope completes an entire orbit in 95 minutes. The angle covered in one entire orbit is
rad
And the time taken is
Therefore, the angular velocity of the telescope is
2)
For an object in circular motion, the relationship between angular velocity and linear velocity is given by the equation
where
v is the linear velocity
is the angular velocity
r is the radius of the circular orbit
In this problem:
is the angular velocity of the Hubble telescope
The telescope is at an altitude of
h = 600 km
over the Earth's surface, which has a radius of
R = 6370 km
So the actual radius of the Hubble's orbit is
Therefore, the linear velocity of the telescope is:
Answer:
The force on q₁ due to q₂ is (0.00973i + 0.02798j) N
Explanation:
F₂₁ =
Where;
F₂₁ is the vector force on q₁ due to q₂
K is the coulomb's constant = 8.99 X 10⁹ Nm²/C²
r₂₁ is the unit vector
|r₂₁| is the magnitude of the unit vector
|q₁| is the absolute charge on point charge one
|q₂| is the absolute charge on point charge two
r₂₁ = [(9-5)i +(7.4-(-4))j] = (4i + 11.5j)
|r₂₁| =
(|r₂₁|)² = 148.25
= 0.050938(0.19107i + 0.54933j) N
= (0.00973i + 0.02798j) N
Therefore, the force on q₁ due to q₂ is (0.00973i + 0.02798j) N