A skydiver of mass 87 kg falls straight down. If air resistance exerts 355 N of force on him as he falls, what is the net force
2 answers:
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1) Displacement: -49 m, in the negative direction
Explanation:
The displacement of an object is a vector, whose magnitude is given by the difference between the final point of the motion and the starting point:
In this problem, the starting point is +34 m, while the final position is -15 m; therefore, the displacement is:
and the direction is negative, in according to the negative sign.
2) Velocity: -3.27 m/s
Explanation:
Velocity is equal to the ratio between the displacement and the time taken:
in this problem, we have:
d = -49 m is the displacement
t = 15 s is the time
therefore, the velocity is
and the direction is negative.
1)
2) 13.9 s
Explanation:
1)
The acceleration due to gravity is the acceleration that an object in free fall (acted upon the force of gravity only) would have.
It can be calculated using the equation:
(1)
where
G is the gravitational constant
is the Earth's mass
r is the distance of the object from the Earth's center
The pendulum in the problem is at an altitude of 3 times the radius of the Earth (R), so its distance from the Earth's center is
where
is the Earth's radius
Therefore, we can calculate the acceleration due to gravity at that height using eq.(1):
2)
The period of a simple pendulum is the time the pendulum takes to complete one oscillation. It is given by the formula
where
L is the length of the pendulum
g is the acceleration due to gravity at the location of the pendulum
Note that the period of a pendulum does not depend on its mass.
For the pendulum in this problem, we have:
L = 3 m is its length
is the acceleration due to gravity (calculated in part 1)
Therefore, the period of the pendulum is: