Two persons are on either sides of a tower of height 150 m. The persons observers the top of the tow

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23 Oct 2020 Heights and Distance

Two persons are on either sides of a tower of height 150 m. The persons observers the top of the tower at an angle of elevation of 45° and 60°. If a car crosses the distance between these two persons in 15 seconds, what is the speed of the car?

OPtion

1) 15.77 km/hr
2) 31.144 km /hr
3) 34.02 km /hr
4) 54.10 km /hr
5) 56.784 m/s
6) 16.784 km /hr
7) 56.10 km /hr
8) 56.784 km /hr
9) 16.63 km /hr
10) None of these

Solution

Let BD be the tower and A and C be the positions of the persons.
Given that BD = 150 m, angle BAD = 45°, angle BCD = 60°

From the right ABD,
tan 45° = BD/BA
=> BD = BA = 150 m

From the right CBD,
tan 60° = BD/BC
=> BC = 150/√3

Distance between the two persons = AC = BA + BC
AC = 150 + 150/√3 = 150 + 86.60 = ~236.60 m

Speed of car = Distance / time = 236.60/15 = 15.77 m/sec = 56.784 km/hr

Option 8)

Correct Option: 8 Best Solution (0)