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## Homework Statement

"A falling object travels one-fourth of its total distance in the last second of its fall. From what height was it dropped?"

Reference: Up is (+)

Scenario 1 (Complete motion)

a = -9.8

v

_{1}= 0

d = -x

v

_{2}= ?

Scenario 2 (Motion at the last second)

a = -9.8

d' = (1/4)(-x)

t' = 1

v

_{2}= ?

## Homework Equations

Complete motion: v

_{2}

^{2}= v

_{1}

^{2}+ 2ad

Motion at the last second: d' = v

_{2}t' - (1/2)(a)(t')

^{2}

3. The Attempt at a Solution

3. The Attempt at a Solution

Setting both equation equal to v

_{2}and then solving for x

**Complete motion:**

v

_{2}

^{2}= v

_{1}

^{2}+ 2ad

v

_{2}

^{2}= (0)

^{2}+ (2)(-9.8)(-x)

v

_{2}

^{2}= (19.6)(x)

v

_{2}= [(19.6)(x)]

^{(1/2)}

**Last second:**

d' = v

_{2}t' - (1/2)(a)(t')

^{2}

(1/4)(-x) = v

_{2}(1) - (-4.9)(1)

^{2}

**Substitution:**

(1/4)(-x) = [(19.6)(x)]

^{(1/2)}- 4.9

[(1/4)(-x)]

^{2}= (19.6)(x) + (-4.9)

^{2}

x

^{2}/ 16 = (19.6)(x) + (-4.9)

^{2}

x

^{2}- (313.6)(x) - 384.16 = 0

x = - 1.22 x = 314.82

Edit: Was a problem with the signs should be

(1/4)(-x) = [(19.6)(x)]

^{(1/2)}+ 4.9

Answer is supposed to be x = 270

Last edited: