A peacock is sitting on the tree and observes its prey on the ground. It makes an angle of depression of `22^(@)` to catch the prey. The speed of the peacock was observed to be 10 km/hr and it catches its prey in 1 min 12 seconds. At what height was the peacock on the tree?
`(cos 22^(@)=0.927, sin 22^(@)=0.374, tan 22^(@)=0.404)`

Roshani saw an eagle on the top of a tree at an angle of elevation of 61^(@) , while she was standing at the door of her house. She went on the terrace of the house so that she could see it clearly. The terrace was at a height of 4m . While observing the eagle from there the angle of elevation was 52^(@) . At what height from the ground was the eagle? tan 61^(@)=1.8, tan 52^(@)=1.28, tan 29^(@)=0.55, tan 38^(@)=0.78)

Roshani saw an eagle on the top of a tree at an angle of elevation of 61^(@) , while she was standing at the door of her house. She went on the terrace of the house so that she could see it clearly. The terrace was at a height of 4m . While observing the eagle from there the angle of elevation was 52^(@) . At what height from the ground was the eagle? tan 61^(@)=1.8, tan 52^(@)=1.28, tann 29^(@)=0.55, tan 38^(@)=0.78)

A tree 12m high, a broken by the wind in such a way that its top touches the ground and makes an angle 60^0 with the ground. At what height from the bottom the tree is broken by the wind?

A circular racetrack of radius 100 m is blanked at an angle of 45 ^(@) . What is the (i) Optimum speed of race car to acoid wear and tear of its tyres ? (ii) Maximum permissible speed to acoid slipping if the coefficient of friction is 0*22 ?

A turn of radius 100 m is banked for a speed of 20 m/s (a) Find the banking angle (b) If a vehicle of mass 500 kg negotiates the curve find the force of friction on it if its speed is – (i) 30 m/s (ii) 10 m/s Assume that friction is sufficient to prevent skidding and slipping. [Take "tan" 22^(@) = 0.4 , "sin" 22^(@) = 0.375 , "cos" 22^(@) = 0.93 , g = 10 ms^(-2) ]

A bicycle is traveling downhill at a high speed. Suddenly, the cyclist sees that a bridge ahead has collapsed, so she has to stop. What is the maximum magnitude of acceleration the bicycle can have if it is not to flip over its front wheel—in particular, if its rear wheel is not to leave the ground? The slope makes an angle of 37^@ with the horizontal. On level ground, the centre of mass of the woman–bicycle system is at a point 1.0 m above the ground, 1.0 m horizontally behind the axle of the front wheel, and 35.0 cm in front of the rear axle. Assume that the tires do not skid.

A bicycle is traveling downhill at a high speed. Suddenly, the cyclist sees that a bridge ahead has collapsed, so she has to stop. What is the maximum magnitude of acceleration the bicycle can have if it is not to flip over its front wheel—in particular, if its rear wheel is not to leave the ground? The slope makes an angle of 37^@ with the horizontal. On level ground, the centre of mass of the woman–bicycle system is at a point 1.0 m above the ground, 1.0 m horizontally behind the axle of the front wheel, and 35.0 cm in front of the rear axle. Assume that the tires do not skid.

An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at a ground observation point by the aircraft positions 10.0 s apart is 30°, what is the speed of the aircraft ? (tan = 15° = 0.2679)