- An impulse is equivalent to
1 answer:
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A) 2.64t
B) 2.64h
C) 2.64D
Explanation:
A)
The motion of the athlete is equivalent to the motion of a projectile, which consists of two independent motions:
- A uniform motion (constant velocity) along the horizontal direction
- A uniformly accelerated motion (constant acceleration) along the vertical direction
The time of flight of a projectile can be found from the equations of motion, and it is found to be
where
u is the initial speed
is the angle of projection
g is the acceleration due to gravity
In this problem, when the athlete is on the Earth, the time of flight is .
When she is on Mars, the acceleration due to gravity is:
where g is the acceleration due to gravity on Earth. Therefore, the time of flight on Mars will be:
B)
The maximum height reached by a projectile can be also found using the equations of motion, and it is given by
where
u is the initial speed
is the angle of projection
g is the acceleration due to gravity
In this problem, when the athlete is on the Earth, the maximum height is .
When she is on Mars, the acceleration due to gravity is:
where g is the acceleration due to gravity on Earth. So, the maximum height reached on Mars will be:
C)
The horizontal distance covered by a projectile is also found from the equations of motion, and it is given by
where:
u is the initial speed
is the angle of projection
g is the acceleration due to gravity
In this problem, when the athlete is on the Earth, the horizontal distance covered is D.
When she is on Mars, the acceleration due to gravity is:
where g is the acceleration due to gravity on Earth. Therefore, the horizontal distance reached on Mars will be:
Answer:
23376 days
Explanation:
The problem can be solved using Kepler's third law of planetary motion which states that the square of the period T of a planet round the sun is directly proportional to the cube of its mean distance R from the sun.
where k is a constant.
From equation (1) we can deduce that the ratio of the square of the period of a planet to the cube of its mean distance from the sun is a constant.
Let the orbital period of the earth be and its mean distance of from the sun be
.
Also let the orbital period of the planet be and its mean distance from the sun be
.
Equation (2) therefore implies the following;
We make the period of the planet the subject of formula as follows;
But recall that from the problem stated, the mean distance of the planet from the sun is 16 times that of the earth, so therefore
Substituting equation (5) into (4), we obtain the following;
cancels out and we are left with the following;
Recall that the orbital period of the earth is about 365.25 days, hence;