# Two ladders that are 10 m in length are inclined to each other at an angle of 45 degrees. A person climbs up one ladder in 90 s and comes down the other in 30 s. What is the velocity of the person.

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The ladders are 10 m in length and inclined to each other at 45 degrees. Velocity is the displacement in unit time. When the person climbs up one ladder and climbs down the other the total distance traveled is 20 m but this is not the displacement of the person.

To find the velocity the displacement has to be found first. As the ladders are inclined to each other at an angle 45 degrees, an isosceles triangle is formed with the angles opposite the equal sides equal to 67.5 degrees. If a horizontal is dropped from the point where the two ladders meet each other, the distance from the base of each ladder to the point where the horizontal meets the ground is given by 10*sin 22.5 = 3.826 m. The total displacement is in the horizontal direction and equal to 7.6536 m. The time taken for this displacement is 90 + 30 = 120 s.

This gives the velocity of the person as 7.6536/120 = 0.0638 m/s.