How is Impulse related to Force?
1 answer:
You might be interested in
Answer:
a) θ=210°, b) t=1.155hr, c) t=1.333hr, d) t=1.333hr, e) θ=180° (straight across), f) t=1hr.
Explanation:
So, the very first thing we nee to do when solving this problem is draw a diagram that represents it. In the attached picture I show a diagram for each part of this problem.
part a)
So, for her to move in a direction directly opposite her starting point, the x-component of her velocity must be de same as the velocity of the river in the opposite direction. We can use this fact to find the angle we need. If we analize the triangle I drew in the diagram, we can ses that:
When solving for theta, we get that:
so now we can substitute the corresponding values:
Which yields:
but we are measuring the angle relative to the line perpendicular to the river, positive if down the river. So we need to subtract the angle from 270° so we get:
θ=270°-60°=210°
part b)
for part b, we need to find what the y-component for the velocity of the boat is for an angle of 210° as shown in the problem, so we get that:
The woman will head in a negative 5.60km distance from one side to the other, so we get that the time it takes her to go to the other side of the river is:
part c)
In order to find the time it takes her to travel 2.80km down and up the river, we need to find the velocities she will have in both directions. First, down stream:
and now up stream:
Once we got these two velocities we will now need to find the time to take each trip:
time down stream:
and the time up stream:
so the total time will be:
d) the time it takes the boat to go upstream and then downstream for the same distance is the same as the time we got on part c, since both times will be the same but they will come in different order, but their sum will be just the same:
t=1.333hr
e) For her to cross the river faster, she must row in a 180° direction (this is in a direction straight accross the river) that way she will use all her velocity to move across the river. (Even though she will move a certain distance horizontally and will not reach a point opposite to the starting point.)
f) In order to find the time it takes her to get to the other side, we need to divide the distance into the velocity of the boat.
so
t= 1hr
The period of a simple pendulum is given by
where
L is the pendulum length
g is the acceleration of gravity
If we move the same pendulum from Earth to the Moon, its length L remains the same, while the acceleration of gravity g changes. So we can write the period of the pendulum on Earth as:
where
is the acceleration of gravity on Earth, while the period of the pendulum on the Moon is
where
is the acceleration of gravity on the Moon.
If we do the ratio of the two periods, we get
but the gravity acceleration on the Moon is 1/6 of the gravity acceleration on Earth, so we can write
and we can rewrite the previous ratio as
so the period of the pendulum on the Moon is
where
L is the pendulum length
g is the acceleration of gravity
If we move the same pendulum from Earth to the Moon, its length L remains the same, while the acceleration of gravity g changes. So we can write the period of the pendulum on Earth as:
where
where
If we do the ratio of the two periods, we get
but the gravity acceleration on the Moon is 1/6 of the gravity acceleration on Earth, so we can write
so the period of the pendulum on the Moon is