An aeroplane flying horizontally 750m above the ground lo an elevation of 60° . After 5 second the elevation is observed 30° . What is the speed of the aeroplane in km per hour?

Question

An aeroplane flying horizontally 750m above the ground lo an elevation of 60° .  After 5 second the elevation is observed 30° . What is the speed of the aeroplane in km per hour?

Emery Adkins · Accepted Answer

The speed is #=623.5kmh^-1#

Let the speed of the plane #=vkmh^-1#

Then,

The distance travelled in #5s# is

#d=v/3.6*5=v/0.72=1.389m#

Let the horizontal distance between the observer and the plane (first observation) be #=xm#

Then,

#tan60=750/x#................................#(1)#

#tan30=750/(x+v/0.72)#...................#(2)#

Eliminationg #x# from equations #(1)# and #(2)#

#x=750/tan60=430.01#

#x+v/0.72=750/tan30=1299.04#

#v/0.72=1299.04-430.01=866.03#

#v=866.03*0.72=623.5kmh^-1#

Grace Ashcraft · Answer

undefined To find the speed of the airplane, we first need to determine the horizontal distance traveled by the airplane during the 5-second interval.

Using trigonometry, we can calculate the horizontal distance traveled by the airplane when the elevation angle changes from 60° to 30°.

First, let's find the initial horizontal distance (d1) using the given information:
tan(60°) = height / horizontal distance
d1 = height / tan(60°)
d1 = 750 / tan(60°)
d1 ≈ 750 / 1.732
d1 ≈ 433.01 meters

Now, let's find the final horizontal distance (d2) using the same method:
tan(30°) = height / horizontal distance
d2 = height / tan(30°)
d2 = 750 / tan(30°)
d2 ≈ 750 / 0.577
d2 ≈ 1298.88 meters

The horizontal distance traveled by the airplane during the 5-second interval is:
Δd = d2 - d1
Δd = 1298.88 - 433.01
Δd ≈ 865.87 meters

Now, we can use the formula: speed = distance / time
speed = Δd / time
speed = 865.87 / 5
speed ≈ 173.17 meters per second

To convert meters per second to kilometers per hour:
1 meter per second ≈ 3.6 kilometers per hour
Therefore:
speed ≈ 173.17 * 3.6
speed ≈ 623.42 kilometers per hour

So, the speed of the airplane is approximately 623.42 kilometers per hour.

HIX Tutor · Answer

undefined To find the speed of the airplane, we need to consider the horizontal and vertical components of its motion.

1. First, let's find the horizontal distance traveled by the airplane in 5 seconds. This distance is equal to the horizontal component of the speed multiplied by time.

2. The initial elevation of 60° forms a right-angled triangle with the ground. We can use trigonometry to find the horizontal component of the speed.

3. Using the trigonometric relationship: cosine(angle) = adjacent/hypotenuse, we have: 
cos(60°) = horizontal speed / total speed
horizontal speed = total speed * cos(60°)

4. Similarly, after 5 seconds, the elevation of 30° forms a right-angled triangle. We can repeat the process to find the new horizontal speed using cos(30°).

5. The change in horizontal distance gives the total horizontal distance traveled in 5 seconds.

6. To convert this distance into kilometers, divide it by 1000.

7. Finally, to find the speed in kilometers per hour, divide the horizontal distance (in km) by the time taken in hours (5 seconds converted to hours).

So, in summary, we calculate the horizontal distances at the two elevations, find the total distance traveled, convert it to kilometers, and then determine the speed in km/hr by dividing the total distance by the time in hours. 🛩📏