Question #b667f

2 Answers
Sahar Mulla ❤
Feb 17, 2018

the plane flies at height, #h=3400m#
angle subtended, #theta=30^@#

#tan theta=("distance travelled in 10s")/h#
#tan 30^@ = x/3400#
#x=1/sqrt3 xx 3400 = 0.58 xx 3400 = 1972m #

now, since
#"speed" = ("distance")/("time")#
#= 1972/10 = 197.2m/s#

anantha n.
Feb 17, 2018

speed = 196.3 m/s

Explanation:

The basic formula you have to use will be
speed = distance travelled / time taken ;
Here we know the time as 10 second .
We have a distance of 3400 m but that is NOT the distance travelled

It is rather the height of the aircraft directly above the observer/observation point at a time enter image source here

The aircraft moves from point A to B in 10 seconds creating an angle of seperation 30 degrees at observation point O .

Using basic trigonometry , we can fin distance AB
From triangle ABO ,

#tan 30^o = (AB)/(OA)#
=> #AB = OA * tan30#
=> #AB = 3400 * 0.5773 = 1963#

So distance AB = 1963 , time taken = 10s
Speed of the aircraft = 1963/10 = 196.3 m/s

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