Answer:
The astronaut's weight will be one-forth of her normal weight on earth.
Explanation:
From Newton's law of gravitation, we can write the acceleration due to gravity (g) on Earth's surface is given by
where 'G' is gravitational constant, '
' is Earth's mass and 'R' is Earth's radius.
As shown in the figure, if the astronaut is at a height 'h' from earth's surface and if '
' be the value of the acceleration due to gravity at that height, then
Taking the ratio of both the equations, and as given h = R.
So,
where 'm' is the mass of the astronaut.
So the weight of the astronaut will be one-forth her normal weight on earth.
-- From the point of view of an observer on Earth, the moon's orbit is an ellipse
with the Earth's center at one focus.
-- From the point of view of an observer on the sun, or on any other planet,
the moon's orbit is an ellipse with the sun at one focus, and perturbed by being
near the Earth.
Answer:
Explanation:
We can try writing the equation of the horizontal component of the length of the minute hand in terms of distance and the angle, that depends of time in this particular case.
The x-component of the length of the minute hand is:
(1)
- d is the length of the minute hand (d=D/2)
- D is the diameter of the clock
- t is the time (min)
Now, using the angular kinematic equations we can express the angle in term of angular velocity and time. As we know, the minute hand moves with a constant angular velocity, so we can use this equation:
(2)
Also we know, that the minute hand moves 90 degrees or π/2 rad in 15 min, so using the definition of angular velocity, we have:
Now, let's put this value on (2)
Finally the length x(t) of the shadow of the minute hand as a function of time t, will be:
I hope it helps you!
Answer:
The acceleration of the cheetahs is 10.1 m/s²
Explanation:
Hi there!
The equation of velocity of an object moving along a straight line with constant acceleration is the following:
v = v0 + a · t
Where:
v = velocity of the object at time t.
v0 = initial velocity.
a = acceleration.
t = time
We know that at t = 2.22 s, v = 50.0 mi/h. The initial velocity, v0, is zero.
Let's convert mi/h into m/s:
50.0 mi/h · (1609.3 m / 1 mi) · (1 h / 3600 s) = 22.4 m/s
Then, using the equation:
v = v0 + a · t
22.4 m/s = 0 m/s + a · 2.22 s
Solving for a:
22.4 m/s / 2.22 s = a
a = 10.1 m/s²
The acceleration of the cheetahs is 10.1 m/s²
