Question : The angle of elevation of an aeroplane from a point on the ground is 60°. After 15 seconds of flight, the elevation changes to 30°. If the aeroplane is flying at a height of $1500\sqrt{3}$ metre, find the speed of the plane:
Option 1: 300 m/sec
Option 2: 200 m/sec
Option 3: 100 m/sec
Option 4: 150 m/sec
Correct Answer: 200 m/sec
Solution : Height of the aeroplane = BD = CE = $1500\sqrt{3}$ m and $\angle$ BAE = 60°, $\angle$ CAE = 30° In $\Delta$ ADB, $\tan 60°=\frac{1500\sqrt{3}}{AD}$ ⇒ $\sqrt{3}=\frac{1500\sqrt{3}}{AD}$ ⇒ AD = $\frac{1500\sqrt{3}}{\sqrt{3}}$ ⇒ AD = 1500 m In $\Delta$ CAE, $\tan 30°=\frac{1500\sqrt{3}}{AE}$ ⇒ $\frac{1}{\sqrt{3}}=\frac{1500\sqrt{3}}{AE}$ ⇒ AE = $1500\sqrt{3}×\sqrt{3}$ ⇒ AE = 4500 m Distance covered by plane in 15 seconds: BC = DE = AE – AD = 4500 – 1500 = 3000 m So, speed of plane = $\frac{3000}{15}$ = 200 m/s Hence, the correct answer is 200 m/sec.
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Question : A pole of length 7 m is fixed vertically on the top of a tower. The angle of elevation of the top of the pole observed from a point on the ground is 60° and the angle of depression of the same point on the ground from the top of the tower is 45°. The height (in m) of
Question : If the angle of elevation of the Sun changes from 30° to 45°, the length of the shadow of a pillar decreases by 20 metres. The height of the pillar is:
Question : From a point 12 m above the water level, the angle of elevation of the top of a hill is 60° and the angle of depression of the base of the hill is 30°. What is the height (in m) of the hill?
Question : A 22 m long ladder (whose foot is on the ground) leans against a wall making an angle of 60° with the wall. What is the height (in m) of the point where the ladder touches the wall from the ground?
Question : If the angle of elevation of a balloon from two consecutive kilometre stones along a road are 30° and 60° respectively, then the height of the balloon above the ground will be:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile