## Question

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})

### Solution

t = 0.59s or 3.41s and 57 m

If the body falls a height h in time t, from 2^{nd} equation of motion we have

now, as the distance fallen in (t – 1)s will be

So from eqns. (1) and (2) distance fallen in the last second

but according to given problem as (h – h’)h/2

t = 0.59s or 3.41s

0.59s is physically unacceptable as it gives the total time t taken by the body to reach ground lesser than one sec while according to the given problem time of motion must be greater than 1s.

t = 3.41s

#### SIMILAR QUESTIONS

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 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

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}?

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}.