A traveler approaches a mountain on highway. He measures the angle of elevation to the peak at each milestone. At two consecutive milestones the angles measured are `4^(@) and 8^(@)`. What is the height of the peak if the distance between consecutive milestones is 1 mile. `(tan 4^(@)=0.0699, tan 8^(@)=0.14405)`

An aeroplane is flying parallel to the Earth's surface at a speed of 175 m/sec and at a height of 600m. The anlge elevation of the aeroplane from a point on the Earth's surface is 37^(@) at a given point. After what period of time does the angle of elevation increase to 53^(@) ? (tan 53^(@)=1.3270, tan 37^(@)=0.7536) .

The electrostatic force on a small sphere of charge 0.4muC due to another small sphere of charge 0.8muC in air is 0.2 N. a. What is the distance between the two spheres? b. What is the force on the second sphere due to the first?

Two waves, each having a frequency of 100 Hz and a wavelength of 2.0 cm, are travelling in the same direction on a string. What is the phase difference between the waves (a) if the second wave was produced 0.015 s later than the first one at the same place, (b) if the two waves were produced at the same instant but the first one was produced a distance 4.0 cm behind the second one ? (c) If each of the waves has an amplitude of 2.0 mm, what would be the amplitudes of the resultant waves in part (a) and (b) ?

A researcher wants to determine the width of a pond from east to west, which cannot by done by actual measurement . From a point p, he finds the distance to the eastern-most point of the pond to be 8 km, while the distance to the western most point from P to be 6 km. if the angle between the two lines of sight is 60^(@) , find the width of the pond.

An electrician wants to repair an electric connection on a pole of height 9 m. He needs to reach 1.8 m below the top of the pole to do repair work. What should be the length of the ladder which he should use, when he climbs it at an angle of 60^(@) with the ground? What will be the distance between foot of the ladder and foot of the pole?

Consider two circles x^2+y^2-4x-6y-8=0 and x^2+y^2-2x-3=0 Statement 1 : Both the circles intersect each other at two distinct points. Statement 2 : The sum of radii of the two circles is greater than the distance between their centers.