# Find the time interval between the above two events.

• 7even
In summary: The helicopter was closer to the submarine at the first firing than it was at the second firing. In summary, at the first firing the helicopter was 9.8m closer to the submarine than it was at the second firing.
7even

## Homework Statement

A foreign fishing submarine moves straight north through Canadian waters at a constant velocity of 12 m/s and a constant depth of 150m below the surface. A Canadian helicopter is in pursuit, flying in exactly the same direction at a constant velocity of 52 m/s and a constant altitude of 550m above the surface. The helicopter, lightly armed, shoots a narrow laser beam which enters the water and strikes the submarine. At one instant, the laser beam leaving the helicopter is directed at an angle of 10° below the horizontal to hit the target. At a later time, the beam has to be tilted down to 30° below the horizontal to maintain contact. Given that the index of refraction is 1.00 for air and 1.33 for water, find the time interval between the above events.

a) 33.3

b) 55.1

c) 68.9

d) 46.7

e) 78

## Homework Equations

n1xsin∅1 = n2xsin∅2

## The Attempt at a Solution

I found the two refractive angles;

1xsin10° = 1.33xsin∅1
∅1 = 7.5°

1xsin30° = 1.33xsin∅2
∅2 = 22.08°

After that, I'm stuck. I have no idea how to use that to find the time interval between each degree.

Last edited:
Hello 7even. Welcome to PF!
In Snell's law are the angles measured from the surface or from the normal to the surface?

From the horizontal, so yes, the surface!

Last edited by a moderator:
I see, so those angles should be changed from 10 to 80 and 30 to 60.

Therefore ∅1 = 47.77° and ∅2=40.63

Yes. good. Consider the first firing of the laser. Can you figure out the horizontal distance between the helicopter and submarine at this instant?

Create a right angle triangle; use the vertical length between the submarine and the helicopter and solve for the horizontal distance.

Therefore, tan10°=700m/x ... x = 3969.9m

No. You're going to need two right triangles. One for the helicopter and one for the submarine.

I see. For the first instant;

tan10°=550m/x ... x = 3,119.2m

tan47.77°=x/150m ... x = 165.25m

So you can figure out the total horizontal distance between the two at the first firing. Repeat for the second firing and see if you can use these distances to determine the time.

Oh I get it, thanks so much for the help!

Last edited:
7even said:
I take the the distances for the first instant and divide each by it's own velocity.

I don't understand why you would do that.

If you were on the submarine how far away horizontally from you was the helicopter at the first firing? How far away horizontally was the helicopter away from you at the second firing? Thus, conclude how much closer the helicopter got (horizontally) to the submarine between the two firings.

## 1. How do you determine the time interval between two events?

To determine the time interval between two events, you need to know the exact time or time period of each event. Then, subtract the starting time from the ending time to calculate the difference. This will give you the time interval between the two events.

## 2. What units are typically used to measure time intervals?

The most common units used to measure time intervals are seconds, minutes, hours, days, weeks, months, and years. However, depending on the length of the time interval, other units such as milliseconds, microseconds, or even centuries may be used.

## 3. Can the time interval between two events be negative?

Yes, the time interval between two events can be negative. This typically occurs when the starting event happens after the ending event. It is important to pay attention to the order of the events when calculating the time interval to avoid a negative result.

## 4. How accurate is the time interval calculated between two events?

The accuracy of the time interval between two events depends on the precision of the starting and ending times provided. The more precise the times are, the more accurate the calculated time interval will be. It is also important to consider any potential sources of error, such as human error in recording the times.

## 5. Can the time interval between two events be calculated if the events occur on different days?

Yes, the time interval between two events can be calculated even if the events occur on different days. The time interval calculation will take into account the number of days between the two events, along with the time within each day. This is commonly done when calculating the duration of an event that spans multiple days.

Replies
15
Views
1K
Replies
4
Views
3K
Replies
6
Views
1K
Replies
2
Views
3K
Replies
6
Views
2K
Replies
2
Views
1K
Replies
5
Views
5K
Replies
7
Views
5K
Replies
2
Views
5K
Replies
4
Views
16K