a man on the top of the Lighthouse observed a Boat coming towards it if we take 10 minutes for angle of depression to change from 30 degree to 45 degree the time taken by the boat to reach the Lighthouse is.
Answers
the Lighthouse is 30cm 443 degree
Answer:
Time taken by the boat to reach the Lighthouse is 13.66 minutes.
Step-by-step explanation:
Let the top of the light house is located at height be H m.
when the angle of depression was 30°, while the ship was at a distance from the lighthouse::
S1 = H cot 30°
= H√3
when the angle of depression was 45°, while the ship was at a distance from the lighthouse::
S2 = H cot 45°
= H
When the angle of depression was 90°, while the ship reach the lighthouse:
S3 = H cot 90°
= 0
Hence, the distance changes from H√3 to H m in 10 minutes
So, the speed of ship is:
V = H√3-H/10 m/min
If the ship should reach the lighthouse, the distance varies from H m to 0:
Therefore,
t = H - 0/V
= 10 H/ H√3-H
= 10/√3-1
= 13.66 minutes.
Hence, time taken by the boat to reach the Lighthouse is 13.66 minutes.
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