two helicopters flying at an altitude of 250 m are 2000m apart when they spot a life raft below. the raft is directly between the two helicopters. the angle of depression from one helicopter to the raft is 37 degrees. the angle of depression from the other helicopter is 49 degrees. both helicopters are flying 170 km/h. how long, to the nearest second, will it take the closer aircraft to reach the raft?

Question

two helicopters flying at an altitude of 250 m are 2000m apart when they spot a life raft below. the raft is directly between the two helicopters. the angle of depression from one helicopter to the raft is 37 degrees. the angle of depression from the other helicopter is 49 degrees. both helicopters are flying 170 km/h. how long, to the nearest second, will it take the closer aircraft to reach the raft?

Answer 1

To solve this problem, we'll use the trigonometric concept of angle of depression and the relative speed of the helicopters.

Let's denote the time it takes for the closer helicopter to reach the raft as "t" (in seconds).

First, we need to calculate the horizontal distance covered by the closer helicopter during time "t". We can do this by multiplying the speed of the helicopter (170 km/h) with the time (t) and converting it to meters:

Distance = Speed × Time
Distance = 170 km/h × (t/3600) h (since 1 hour = 3600 seconds)
Distance = (170t) / 3600 (in meters)

Next, we need to find the vertical distance (or the difference in altitude) between the closer helicopter and the raft. We can use the tangent function of the angle of depression (37 degrees) to find this distance:

Vertical Distance = Altitude × tan(Angle of Depression)
Vertical Distance = 250 m × tan(37 degrees)

Now, we can calculate the distance between the closer helicopter and the raft using the Pythagorean theorem:

Distance² = (horizontal distance)² + (vertical distance)²
(2000 + Distance)² = ((170t) / 3600)² + (250 × tan(37 degrees))²

Lastly, we solve this equation to find the value of "t".

Please note that calculating this equation might get complex, and it may be easier to use numerical methods or a calculator to find the value of "t."

Answer 2

To find the time it takes for the closer aircraft to reach the raft, we need to find the distance between the closer aircraft and the raft and then divide it by the speed of the aircraft.

Let's start by finding the distance between the closer aircraft and the raft. We can use trigonometry and the angle of depression from the closer helicopter to the raft.

Since the angle of depression is the angle formed between the line of sight from the helicopter to the raft and a horizontal line, we can use the tangent function to calculate the distance.

We have the following information:
- Altitude of the helicopters: 250 m
- Distance between the helicopters: 2000 m
- Angle of depression from the closer helicopter: 37 degrees

First, we can find the distance between the closer helicopter and the raft using the tangent function:

tan(angle of depression) = opposite / adjacent

tan(37 degrees) = 250 / distance

Rearranging the equation to get the distance:

distance = 250 / tan(37 degrees)

Now, let's calculate this value:

distance = 250 / tan(37 degrees) ≈ 373.66 m

Next, we need to calculate the time it takes for the closer aircraft to reach the raft. We can use the formula:

time = distance / speed

Given that the speed of the aircraft is 170 km/h, we need to convert it to meters per second:

speed = 170 km/h * (1000 m / 1 km) * (1 h / 3600 s) ≈ 47.22 m/s

Now, let's calculate the time:

time = 373.66 m / 47.22 m/s ≈ 7.91 s

Therefore, it will take the closer aircraft approximately 7.91 seconds to reach the raft.

Answer 3

Sin49 = h/d1 = 250m/d1.

d1 = 250/Sin49 =331.3m = Distance of 1st helicopter.

Sin37 = h/d2 = 250/d2
d2 = 250/Sin37 = 415.4m = Distance of
2nd helicopter.

d1 = r*t, t = d1/r =0.3313km / 170km
= 0.00195h = 0.00195h * 3600s/h =
7 Seconds.