A ladder rests against a wall at an inclination `alpha` to the horizontal. Its foot is pulled away from the wall through a distance p so that its upper end slides a distance q down the wall and then the ladder makes an angle `beta` to the horizontal. Show that `(p)/(q)= (cos beta -cos alpha)/(sin alpha- sin beta)`

A ladder 5 cm long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 cm away from the wall ?

Find distance PQ between the points P ( a cos alpha, a sin alpha) and Q ( a cos beta, a sin beta) .

A ladder rests against a frictionless vertical wall, with its upper end 6 m above the ground and the lower end 4 m away from the wall. The weight of the ladder is 500 N and its CG at 1//3^(rd) distance from the lower end. Wall's reaction will be (in newton)

A ladder 20 feet long is leaning against a wall. The bottom of the ladder is 16 feet away from the wall. If the upper end of the ladder slide along wall is lambda times the lower end of the ladder pull along the ground. Find the value of lambda .

A ladder is placed against a wall such that its foot is at a distance of 2.5 cm from the wall and its top reaches a window 6 m above the ground. Find the length of the ladder.

On end of a light spring of natural length d and spring constant k is fixed on a rigid wall and the other is attached to a smooth ring of mass m which can slide without friction on a vertical rod fixed at a distance d from the wall. Initially the spring makes an angle of 37^@ with the horizontal. as shown in figure. When the system is released from rest, find the speed of the ring when the spring becomes horizontal. (sin 37^@=3/5) .

A ball is suspended by a thread of length l at the point O on an incline wall as shown. The inclination of the wall with the vertical is α.The thread is displaced through a small angle β away from the vertical and the ball is released. Find the period of oscillation of pendulum. Consider both cases a. alpha gt beta b. alpha lt beta Assuming that any impact between the wall and the ball is elastic.

The angle of elevation of the top of a tower from a point P on the ground is alpha . After walking a distance of d m towards the foot of the tower, the angle of elevation of the top of the tower is found to be beta . Then, ………..holds good.

One end of a light spring of natural length 4m and spring constant 170 N/m is fixed on a rigid wall and the other is fixed to a smooth ring of mass (1)/(2) kg which can slide without friction in a verical rod fixed at a distance 4 m from the wall. Initially the spring makes an angle of 37^(@) with the horizontal as shown in figure. When the system is released from rest, find the speed of the ring when the spring becomes horizontal.

A Rajput soldier sits on a horse next to a river. Across the river there is a hill and atop the hill is a fortress. He sees a Mughal. Sitting on the fortress's top wall. There is a full moon, so he angrily shoots an arrow at an angle 53^(@) relative to the horizontal. The arrow hits Mughal after a 2 second flight. The horizontal distance from Rajput to Mughal is 30 meters. The arrow is 3 meters above the river when Rajput shoots it. (a) What is the original velocity , vec(V) , of the arrow when Rajput shoots it ? (b) What is Mughal elevation above the river ? (c) What is the flight direction of the arrow the instant before it strikes Mughal, i.e., what is the angle, theta , between its direction and the horizontal when it skins into Mughal's tender flesh ?