When a partical is projected from a tower of height - h- with horizontal with velocity - u- at an angle - - above the horizontal- then range of particle -on ground- is- - ucos- g - u - 2 sin - 2 - g - 2 - 2h g - ucos- - usin- g - u - 2 sin - 2 - g - 2 - 2h g - ucos- u - 2 sin - 2 - g - 2 - - u - 2 sin - 2 - g - 2 - 2h g - cos- u - 2 sin - 2 - g - 2-

The correct option is B [ usinθ g +√( u ^ 2 sin ^ 2 θ g ^ 2 + 2h g )] ucosθ Apply kinematic equation of motion. #10; #10; v^2 u^2=2as #10; ...

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Byju's Answer

Standard XII

Physics

Power, Force and Velocity

When a partic...

Question

When a partical is projected from a tower of height $h$ with horizontal with velocity $u$ at an angle $θ$ above the horizontal, then range of particle (on ground) is

[\frac{u cos θ}{g} + \sqrt{\frac{u^{2} {sin}^{2} θ}{g^{2}} + \frac{2 h}{g}}] u cos θ

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[\frac{u sin θ}{g} + \sqrt{\frac{u^{2} {sin}^{2} θ}{g^{2}} + \frac{2 h}{g}}] u cos θ

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\frac{u^{2} {sin}^{2} θ}{g^{2}} + [\sqrt{\frac{u^{2} {sin}^{2} θ}{g^{2}} + \frac{2 h}{g}}] cos θ

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\frac{u^{2} {sin}^{2} θ}{g^{2}}

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Solution

The correct option is B $[\frac{u sin θ}{g} + \sqrt{\frac{u^{2} {sin}^{2} θ}{g^{2}} + \frac{2 h}{g}}] u cos θ$
Apply kinematic equation of motion.

$v^{2} - u^{2} = 2 a s$

$v = \sqrt{{(- u sin θ)}^{2} + 2 g h}$

Apply kinematic equation of motion

$V = U + a t$

$t = \frac{V - U}{a} = \frac{1}{g} (\sqrt{{(- u sin θ)}^{2} + 2 g h} - (- u sin θ))$

$t = (\sqrt{\frac{u^{2} {sin}^{2} θ}{g^{2}} + \frac{2 h}{g}} + \frac{u sin θ}{g})$

Range, $R = u cos θ \times t = u cos θ (\sqrt{\frac{u^{2} {sin}^{2} θ}{g^{2}} + \frac{2 h}{g}} + \frac{u sin θ}{g})$

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When a partical is projected from a tower of height h with horizontal with velocity u at an angle θ above the horizontal, then range of particle (on ground) is

The correct option is B [usinθg+√u2sin2θg2+2hg]ucosθApply kinematic equation of motion. v2−u2=2as v=√(−usinθ)2+2gh Apply kinematic equation of motion V=U+at t=V−Ua=1g(√(−usinθ)2+2gh−(−usinθ)) t=(√u2sin2θg2+2hg+usinθg) Range, R=ucosθ×t=ucosθ(√u2sin2θg2+2hg+usinθg)

When a partical is projected from a tower of height $h$ with horizontal with velocity $u$ at an angle $θ$ above the horizontal, then range of particle (on ground) is