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Standard XII

Physics

Relative Velocity in 2D

An object lau...

Question

An object launched straight up into the air is said to have parabolic motion (because it goes up, reaches a maximum height, and then comes back down). The height (h) of a projectile at time t is given by the equation $h = \frac{1}{2} g t^{2} + u t + h_{0}$ , where g is the acceleration due to gravity and $u$ and $h_{0}$ are the object's initial velocity and initial height, respectively. Which of the following equations correctly represents the object's acceleration due to gravity in terms of the other variables?

g = \frac{h - u t - h_{0}}{t}

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g = \frac{h - u t - h_{0}}{2 t^{2}}

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g = \frac{2 (h - u t - h_{0})}{t^{2}}

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g = t \sqrt{2 (h - u t - h_{0})}

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Solution

The correct option is D $g = \frac{2 (h - u t - h_{0})}{t^{2}}$
$h = \frac{1}{2} g t^{2} + u t + h_{0}$
$\Rightarrow 2 h = g t^{2} + 2 u t + h u_{0}$
$\Rightarrow g t^{2} = 2 h - 2 u t - 2 h_{0}$
$\Rightarrow g = \frac{2 (h - u t - h_{0})}{t^{2}}$

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Moon	$1.6$
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The correct option is D g=2(h−ut−h0)t2h=12gt2+ut+h0⇒2h=gt2+2ut+hu0⇒gt2=2h−2ut−2h0⇒g=2(h−ut−h0)t2

The correct option is D $g = \frac{2 (h - u t - h_{0})}{t^{2}}$
$h = \frac{1}{2} g t^{2} + u t + h_{0}$
$\Rightarrow 2 h = g t^{2} + 2 u t + h u_{0}$
$\Rightarrow g t^{2} = 2 h - 2 u t - 2 h_{0}$
$\Rightarrow g = \frac{2 (h - u t - h_{0})}{t^{2}}$