The helicopter is traveling at a speed of 35.64 meters per second, calculated by using the sine of a 30° angle within a 30-60-90 right triangle where the altitude of the helicopter formed the hypotenuse.
To find the speed of the helicopter, we need to determine the distance it travels between the two positions subtending a 30° angle to the observation point on the ground, and then divide that distance by the time it took to travel that distance (100 seconds in this case).
Since the angle subtended by the two positions of the helicopter is 30°, we can use the concept of a 30-60-90 right triangle, where the distance between the two positions of the helicopter will be the opposite side of the 30° angle and the distance from the ground point to the helicopter will be the hypotenuse.
Let's denote the distance between the two positions of the helicopter as 'd'. Given that the altitude of the helicopter is 3564m, we can write the following equation using the sine of 30°:
sin(30°) = opposite/hypotenuse
0.5 = d/(2 * 3564m)
d = 0.5 * 2 * 3564m
d = 3564m
Now, the speed of the helicopter (v) can be calculated by dividing the distance by the time:
v = d/t
v = 3564m / 100s
v = 35.64 m/s
Therefore, the helicopter is traveling at a speed of 35.64 meters per second.
The probable question may be:
A helicopter is flying at 3564m above ground. If an angle of 30∘ is subtended at a ground point by the helicopter position 100 apart, what is the speed of the helicopter?