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A hot air balloon rising straight up fro...

A hot air balloon rising straight up from a level field is tracked by a range finder 500 ft from the lift-off point. At the moment the range finder's elevation angle is `pi/4`, the angle is increasing at the rate of 0.14 rad/min. How fast is the balloon rising at that moment.

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The correct Answer is:
`140 ft//min`
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A hot air balloon rising straight up from a level field is tracked by a range finder 500 ft from the lift-off point. At the moment the range finder's elevation angle is (pi)/(4) . The angle is increasing at the rate of 0.14 rad/min. How fast is the balloon rising at the moment ?

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A balloon leaves from a point P rises at a uniform speed. After 6 minutes, an observer situated at a distance of 450 sqrt""3 metres from point P observes that angle of elevation of the balloon is 60^(@) Assume that point of observation and point P are on the same level. What is the speed (in m/s) of the balloon?

A balloon leaves from a point P rises at a uniform speed. After 6 minutes, an observer situated at a distance of 450 sqrt3 metres from point P observes that angle of elevation of the balloon is 60^@ .Assume that point of observation and point P are on the same level. What is the speed (in m/s) of the balloon? एक मुब्बारा एक समान गति से बिन्दु P से छोड़ा जाता है। 6 मिनट पश्चात, बिन्दु P से 450 sqrt3 मीटर दूरी पर एक समीक्षक है जो देखता है कि गुब्बारे का उन्नयन कोण 60^@ है। मान लीजिए कि समीक्षा बिन्दु तथा बिन्दु P एक ही स्तर पर है। गुब्बारे की गति [मी/ से.में] क्या है?

Mr. Naik is a paramilitary Intelligence Corps officer who is tasked with planning a coup on the enemy at a certain date. Currently he is inspecting the area standing on top of the cliff. Agent Vinod is on a hot air balloon in the sky. When Mr. Naik looks down below the cliff towards the sea, he has Ajay and Maran in boats positioned to get a good vantage point. The main goal is to scope out the range and angles at which they should train their soldiers. If the vertical height of the balloon from the top of the cliff is 12 m and angleb=30^(@) , then the distance between the Naik and vinod is

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Rishu is riding in a hot air balloon. After reaching a point P, he spots a car parked at Bon the ground at an angle of depression of 30^@ . The balloon rises further by 50 metres and now he spots the same car at an angle of depression of 45^(@) and a lorry parked at B' at an angle of depression of 30^@ . (Use sqrt3 = 1.73) The measurement of Rishu facing vertically is the height. Distance is defined as the measurement of car/lorry from a point in a horizontal direction. If an imaginary line is drawn from the observation point to the top edge of the car/lorry, a triangle is formed by the vertical, horizontal and imaginary line. The height of the balloon at point P' and distance AB are related as:

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