An object is thrown vertically from a height of $9 m$ $9 m$ at $24 \frac{m}{s}$ $24 m/s$ . How long will it take for the object to hit the ground?

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An object is thrown vertically from a height of $9 m$ $9 m$ at $24 \frac{m}{s}$ $24 m/s$ . How long will it take for the object to hit the ground?

1 Answer

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Answer 1 · 2016-06-02T01:06:27

I found: $5.2 s$ $5.2s$

Explanation:

I would suppose that the velocity is in the upwards direction because it is positive and so in:

$y_{f} - y_{i} = v_{i} t + \frac{1}{2} a t^{2}$ $y_f-y_i=v_it+1/2at^2$
with:
$y_{f} = 0$ $y_f=0$ the ground
$a = g$ $a=g$ downwards.

we have:

$0 - 9 = 24 t - \frac{1}{2} \cdot 9.8 t^{2}$ $0-9=24t-1/2*9.8t^2$
$4.9 t^{2} - 24 t - 9 = 0$ $4.9t^2-24t-9=0$

Using the Quadratic Formula:
$t_{1, 2} = \frac{24 \pm \sqrt{576 + 176.4}}{9.8} =$ $t_(1,2)=(24+-sqrt(576+176.4))/9.8=$
$t_{1, 2} = \frac{24 \pm 27.4}{9.8} =$ $t_(1,2)=(24+-27.4)/9.8=$
$t_{1} = 5.2 s$ $t_1=5.2s$
$t_{2} = - 0.3 s$ $t_2=-0.3s$

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An object is thrown vertically from a height of $9 m$ $9 m$ at $24 \frac{m}{s}$ $24 m/s$ . How long will it take for the object to hit the ground?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

An object is thrown vertically from a height of 9m9 m at 24ms 24 m/s. How long will it take for the object to hit the ground?

1 Answer

Explanation:

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An object is thrown vertically from a height of $9 m$ $9 m$ at $24 \frac{m}{s}$ $24 m/s$ . How long will it take for the object to hit the ground?