IIT JEE , AIEEE Forum - Physics , Mechanics

nsv_j89

A heavy stone is thrown from a cliff of height h with a speed v. The stone will hit the ground with maximum speed if it is thrown

(a) vertically downwards

(b) vertically upwards

(c) horizontally

(d) the speed does not depend on the initial direction

PLEASE EXPLAIN

akhil_o

vertically downward

akhil_o

final velocity is V

V²=v(sin A) ²+2gh, whre A is angle with horizontal

now if V is to be maximum

sin A is max and at -pi/2

unni_enter

d)is the correct option

Applying work energy theorem

since no friction,pseudo or external force is applied the total mechanical energy remains conserved

so taking cliff as 0 potential

1/2 m(v1)^2=1/2m(mv2)^2-mgh(v='SPEED' of body at 2 pts)

using kinematics also u get the same result whether thrown up,down or horizontal

kavindra

arey bhai simple vector addition...ans. both a and b would give the same answer[if air resistance is neglected] if it is thrown horizontally, the horizontal component of velocity remains constant and the vertical component is derived from free fall that is equal to "gt" [v=u +at]
vector addition gives something lesser than v + gt which can be got only by adding them along a straight line.

tarun_bits

throw it any way ....if you conserve the mechanical energy you will see that the speed at bottom is always the same

spideyunlimited

mgh = 1/2 mv^2
so if u neglect air resistance, it will hit with same speed in all cases.

chetan_kp

ya there is a confusion that 1st and 2nd options are right but not the 3rd
; but actually final velocity is same in all the cases coz when u throw horizontally there is a horizontal component present , so the vector sum of both horizontal and vertical components give the same magnitude as that of 1st and 2nd, nudge if wrong

computer001

let it b thrown at

with v

comp in hor is vcos and vertical is vsin

vcos will not get affected as no chang in hor vel

in vertical vel becomes root of(v²sin²

+2gh)

at bottom vel is root of v_x²+ v_y² root of (v^2(sin^2 + cos^2) + 2gh) which is root of (v^2 + 2gh) which is indep of the angle of throwing so for all angles same vel at bottom

bhartibhanushali

let E be energy transferred to stone when is thrown
case 1) when it is thrown upwards stone uses its E against gravity
when this E =0 stone reaches max height n starts coming downward such that its K.E increases n it becomes E when total displacement is 0 {at height h} more over it starts to move downward
such that it K.E increases by X
hence total K.E energy is E+X
we get velocity from this
case 2) when it is thrown vertically downwards its k.e increases by x
as in above case
hence total ke is E+x
case 3) when it is thrown horizontally from height h{since perpendicular distance is still h} k.e. still increses by x
hence its k.e is E+x

hence in short by law of conservation of energy its D

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