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 $h=\frac{1}{2}g{t}^2+ut+h_0$, 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?

• A. $g=\frac{h-ut-h_0}{t}$
• B. $g=\frac{h-ut-h_0}{2t^2}$
• C. $g=\frac{2(h-ut-h_0)}{t^2}$
• D. $g=t\sqrt{2(h-ut-h_0)}$

Answer 1

Answer: (C)

$g=\frac{2(h-ut-h_0)}{t^2}$

$h=\frac{1}{2}g{t}^2+ut+h_0$

$\Rightarrow 2h=g{t}^2+2ut+h{u}_0$

$\Rightarrow g{t}^2=2h-2ut-2h_0$

$\Rightarrow g=\frac{2(h-ut-h_0)}{t^2}$