The maximum height attained by a projectile is increased by $$10$$% by increasing its speed of projection, without changing the angle of projection. The percentage increase in the horizontal range will be

Question

Infinity Learn · Accepted Answer

we know that $$h=u2sin2$$⁡θ$$2gLet$$ δh be increase in h when u changes by δu. Henceδ$$h=2u$$δ$$usin2$$⁡θ$$2gor$$         δ$$hh=2$$δuuaGiven that h is increased by $$10$$%, i.e., δ$$h/h=0$$⋅$$1$$ So,         $$0$$⋅$$1=2$$δuu                   …. (1)Further$$,    $$R=u2sin$$⁡$$2$$θgor                 δ$$R=2u$$δusin⁡$$2$$θg    So,             δ$$RR=2$$δuu              …… $$(2)From$$ eqs. $$(1) and (2), we getδ$$RR=0$$⋅$$1$$  or  δ$$R=0$$⋅$$1$$×RHence R is also increased by $$10$$%.

The maximum height attained by a projectile is increased by 10% by increasing its speed of projection, without changing the angle of projection. The percentage increase in the horizontal range will be

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