## Question

A body starting from rest slides on an inclined plane of length *s* as shown in Fig. Calculate the time of descent and speed at the bottom. Find also

(a) Distance covered in half the time of descent and (b) time taken to cover half the distance

### Solution

s' = *s*/4 and

When a body slides on a inclined plane, component of weight along the plane produces acceleration

So, equation of motion can be applied. From 2^{nd} equation of motion, here

While from 3^{rd} equation of motion,

*v*^{2} = 0^{2} + 2(g sin *θ*)s

Eqns. (2) and (3) are the desired result. Further as from Eqn. (1)

i.e., in half the time of descent the body covers only one-fourth of the total distance.

i.e., in about 0.7 times the time of decent the body covers half of the total distance.

#### SIMILAR QUESTIONS

A particle starts moving from the position of rest under a constant acc. If it travels a distance *x* in *t* sec, what distance will it travel in next *t* sec?

A particle moving with velocity equal to 0.4 *m/s* is subjected to an acceleration of* * 0.15 *m/s*^{2} for 2 sec in a direction at right angle to its direction of motion. What is the magnitude of resultant velocity?

Two particles *A* and *B* move with constant velocities *v*_{1} and *v*_{2} along two mutually perpendicular straight lines towards the intersection point *O*. At moment *t* = 0 the particle were located at distances *l*_{1} and *l*_{2} from O respectively. Find the time when they are nearest and also this shortest distance.

A juggler throws balls into air. He throws one whenever the previous one is at its highest point. How high do the balls rise if the throws n balls each sec? Acceleration due to gravity is g.

A pebble is thrown vertically upwards from a bridge with an initial velocity of 4.9m/s. It strikes the water after 2s. If acc. Due to gravity is 9.8m/s^{2} (a) what is the height of the bridge?(b) with what velocity does the pebble strike the water?

A body is released from a height and falls freely towards the earth. Exactly 1 sec later another body is released. What is the distance between the two bodies 2 sec after the release of the second body, if g = 9.8m/s^{2}?

If a body travels half its total path in the last second of its fall from rest, find; (a) the time and (b) the height of fall. Explain the physically unacceptable solution of the quadratic time equation. (g = 9.8m/s^{2})

A stone is dropped into a well and the sound of impact of stone on the water is heard after 2.056 sec of the release of stone from the top. If acc. Due to gravity is 980cm/sec^{2} and velocity of sound in air is 350m/s, calculate the depth of the well.

A person aims a gun at a target located at a horizontal distance of 100 m. If the gun imparts a horizontal speed of 500 ms^{-1} to the bullet, at what height above the target must he aim his gun in order to hit it? Take *g* = 10 ms^{-2}.