Question : The angle of elevation of an aeroplane from a point on the ground is 60°. After flying for 30 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a height of 4500 metres, then what is the speed (in m/s) of an aeroplane?

Option 1: $50\sqrt3$

Option 2: $100\sqrt3$

Option 3: $200\sqrt3$

Option 4: $300\sqrt3$

Question : The angles of elevation of an aeroplane flying vertically above the ground, as observed from the two consecutive stones,1 km apart, are 45° and 60°. The height of the aeroplane above the ground in km is:

Option 1: $(\sqrt{3}+1)$

Option 2: $(\sqrt{3}+3)$

Option 3: $\frac{1}{2}(\sqrt{3}+1)$

Option 4: $\frac{1}{2}(\sqrt{3}+3)$

Question : An aeroplane flying horizontally at a height of 3 km above the ground is observed at a certain point on earth to subtend an angle of $60^\circ$. After 15 seconds of flight, its angle of elevation is changed to $30^\circ$. The speed of the aeroplane (Take $\sqrt{3}=1.732$) is:

Option 1: 230.63 m/s

Option 2: 230.93 m/s

Option 3: 235.85 m/s

Option 4: 236.25 m/s

Question : The angle of elevation of an aeroplane as observed from a point 30 metres above the transparent water surface of a lake is 30° and the angle of the depression of the image of the aeroplane in the water of the lake is 60°. The height of the aeroplane from the water surface of the lake is:

Option 1: 60 metres

Option 2: 45 metres

Option 3: 50 metres

Option 4: 75 metres

Question : The shadow of a tower when the angle of elevation of the sun is 45°, is found to be 10 metres longer than when it was 60°. The height of the tower is:

Option 1: $5\sqrt{3}-1$ metres

Option 2: $5(3+\sqrt{3})$ metres

Option 3: $10(\sqrt{3}-1)$ metres

Option 4: $10(\sqrt{3}+1)$ metres