ii. A stone thrown vertically upwards with initial velocity u reachesa

1.	ii. A stone thrown vertically upwards with initial velocity u reachesa height 'h'before coming down. Show that the time taken to goup is same as the time taken to come down.
Answer» Let us consider an object which is projected vertically upwards with initial velocity u which reaches a maximum height h.Acceleration due to gravity=-gEquation of Motion for a body projected thrown upwards :V=u-gt----------(1)h=ut-1/2gt² -----------(2)v²-u²=-2gh --------(3) Equations of motion for freely falling body :for free fall :Initial velocity=u=0g=gV=gt----------(4)h=1/2gt²-------(5)v²=2gh------(6)Time of Ascent is the time taken by body thrown up to reach maximum height hAt maximum height , V=0 Equation (1) turns to u=gt1t1=u/g ----------(7)Maximm height h=u²/2g ----------(8) Time of descent : After reaching maximum height , the body begins to travel downward like free fallso equation (5) h=1/2gt₂²t₂²=2h/gt₂=√2h/gbut from equation (9)t₂=√2xu²/2g²t₂=u/g -----------------equation (10)∴t₁=t₂The time ascent is equal to time of descent in case of bodies moving under gravity.

ii. A stone thrown vertically upwards with initial velocity u reachesa height 'h'before coming down. Show that the time taken to goup is same as the time taken to come down.

Answer»

Let us consider an object which is projected vertically upwards with initial velocity u which reaches a maximum height h.Acceleration due to gravity=-gEquation of Motion for a body projected thrown upwards :V=u-gt----------(1)h=ut-1/2gt² -----------(2)v²-u²=-2gh --------(3)

Equations of motion for freely falling body :for free fall :Initial velocity=u=0g=gV=gt----------(4)h=1/2gt²-------(5)v²=2gh------(6)Time of Ascent is the time taken by body thrown up to reach maximum height hAt maximum height , V=0

Equation (1) turns to u=gt1t1=u/g ----------(7)Maximm height h=u²/2g ----------(8)

Time of descent : After reaching maximum height , the body begins to travel downward like free fallso equation (5) h=1/2gt₂²t₂²=2h/gt₂=√2h/gbut from equation (9)t₂=√2xu²/2g²t₂=u/g -----------------equation (10)∴t₁=t₂The time ascent is equal to time of descent in case of bodies moving under gravity.

ii. A stone thrown vertically upwards with initial velocity u reachesa height 'h'before coming down. Show that the time taken to goup is same as the time taken to come down.

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