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Projectile Time, Height and Range

The height an...

Question

The height and horizontal distance $x$ of a projectile are given by $y = (8 t - 5 t^{2}) m$ and $x = 6 t m$ where $t$ is in seconds. Find the maximum height of a projectile.
(Take $g = 10 m / s^{2}$ )

A

4.7 m

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B

5.6 m

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C

3.2 m

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D

8.7 m

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Solution

The correct option is C $3.2 m$
Compare the equation $y = 8 t - 5 t^{2} m$ from first equation of motion in $y$ - direction,
$y = u_{y} t + \frac{1}{2} g t^{2}$
$\Rightarrow u_{y} = 8 m / s$
Since maximum height reached, $H = \frac{u_{y}^{2} {sin}^{2} θ}{2 g}$
We know maximum height is achieved when $θ = 90^{o}$
$H = \frac{u_{y}^{2}}{2 g} = \frac{8^{2}}{20} = 3.2 m$

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