a moving boat is observed from the top of a 150m high cliff moving away from the cliff.The angle of dipression of the boat changes from 60° to45° in 2 min . Find the speed of the boat in m/h.
Answers
find the distance of boat from cliff when angle of elevation is 60° by taking tan60 = height of cliff /distance between boat and cliff it is found that it is
now in the same way taking angle of elevation as 45°find distance of boat when it is 45 °from the cliff. on finding distance = 150 m
now find the distances between two position of boats
which is
= 50(3 -1.732) = 63.4
the boat travels 63.4 m in 2 min or 120 sec
:. speed of boat = distance / time itis wanted m/hr
:. answer should be multiplied by 3600
=63.4×3600/120 =1902 m/hr
Answer:
1901.925 m/h
Explanation:
The scenario is shown in the image below.
Height of Cliff = AB = 150 m
In triangle ADB,
tan 45 = AB / DB
1 = 150 m / DB
DB = 150 m
Also, in triangle, ACB,
tan 60 = AB / AC
√3 = 150 m / AC
AC = 150 / √3 m = 86.6025 m
So, DC = 150 m - 86.6025 m = 63.3975 m
Time = 2 min = 2/60 = 1/30 h
So. Speed = D / T = 63.3975 m / (1/30 h) = 1901.925 m/h
