A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point
Solution:
Let the height of the tower be AD and the starting point of the car be at point B and after 6 seconds let the car be at point C. The angles of the depression of the car from the top A of the tower at point B and C are 30° and 60° respectively.
Distance travelled by the car from the starting point towards the tower in 6 seconds = BC
Distance travelled by the car after 6 seconds towards the tower = CD
We know that, speed = distance / time
The speed of the car is calculated using the distance BC and time = 6 seconds.
Using Speed and Distance CD, the time to reach foot can be calculated.
In ΔABD,
tan 30° = AD/BD
1/√3 = AD/BD
BD = AD√3 ....(1)
In ΔACD,
tan 60° = AD/CD
√3 = AD/CD
AD = CD√3 ....(2)
From equation (1) and (2)
BD = CD√3 × √3
BC + CD = 3CD [∵ BD = BC + CD]
BC = 2CD ....(3)
Distance travelled by the car from the starting point towards the tower in 6 seconds = BC
Speed of the car to cover distance BC in 6 seconds = Distance/Time
= BC/6
= 2CD/6 [from (3)]
= CD/3
Speed of the car = CD/3 m/s
Distance travelled by the car from point C, towards the tower = CD
Time to cover distance CD at the speed of CD/3 m/s
Time = Distance/speed
= CD / CD/3
= CD × 3 / CD
= 3
The time taken by the car to reach the foot of the tower from point C is 3 seconds.
☛ Check: NCERT Solutions for Class 10 Maths Chapter 9
Video Solution:
A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point
Maths NCERT Solutions Class 10 Chapter 9 Exercise 9.1 Question 15
Summary:
If a straight highway leads to the foot of a tower and a man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed and six seconds later, the angle of depression of the car is found to be 60°, then the time taken by the car to reach the foot of the tower from this point is 3 seconds.
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