d. A stone thrown vertically upwards witinitial velocity u reaches a height 'h'before coming down. Show that thetime taken to go up is same as the timetaken to come down.

d. A stone thrown vertically upwards witinitial velocity u reaches a h

1.	d. A stone thrown vertically upwards witinitial velocity u reaches a height 'h'before coming down. Show that thetime taken to go up is same as the timetaken to come down.
Answer» <p>Let us consider an object which is projected vertically upwards with initial velocity u which reaches a maximum height h.</p><p>Acceleration due to gravity=-g</p><p>Equation of Motion for a body projected thrown upwards :</p><p>V=u-gt----------(1)h=ut-1/2gt² -----------(2)v²-u²=-2gh --------(3)</p><p>Equations of motion for freely falling body :for free fall :Initial velocity=u=0g=gV=gt----------(4)h=1/2gt²-------(5)v²=2gh------(6)</p><p>Time of Ascent is the time taken by body thrown up to reach maximum height hAt maximum height , V=0</p><p>Equation (1) turns to u=gt1</p><p>t1=u/g ----------(7)Maximm height h=u²/2g ----------(8)</p><p>Time of descent : After reaching maximum height , the body begins to travel downward like free fall</p><p>so equation (5) h=1/2gt₂²t₂²=2h/gt₂=√2h/gbut from equation (9)t₂=√2xu²/2g²t₂=u/g -----------------equation (10)</p><p>∴t₁=t₂</p><p>The time ascent is equal to time of descent in case of bodies moving under gravity.</p> <p>thank you</p>