Hugo lies on top of a building, throwing pennies straight down to the street below. The formula for the height $H$ , that a penny falls is $H = V t + 5 t^{2}$ , where $V$ is the original velocity of the penny (how fast Hugo throws it when it leaves his hand) and $t$ is equal to the time it takes to hit the ground. The building is $60$ metres high, and Hugo throws the penny down at an initial speed of $20$ meters per second. How long does it take for the penny to hit the ground,

2

sec

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4

sec

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3

sec

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6

sec

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Solution

The correct option is A $2$ sec
$H = V t + 5 t^{2}$
$60 = 20 t + 5 t^{2}$
$5 t^{2} + 20 t - 60 = 0$
$5 (t^{2} + 4 t - 12) = 0$
$5 (t + 6) (t - 2) = 0$
$t + 6 = 0$ OR $t - 2 = 0$
$t = - 6$ or $t = 2$
Since a time must be positive, discard the negative value for $t$ .

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The correct option is A 2 secH=Vt+5t260=20t+5t25t2+20t−60=05(t2+4t−12)=05(t+6)(t−2)=0t+6=0 OR t−2=0t=−6 or t=2Since a time must be positive, discard the negative value for t.

The correct option is A $2$ sec
$H = V t + 5 t^{2}$
$60 = 20 t + 5 t^{2}$
$5 t^{2} + 20 t - 60 = 0$
$5 (t^{2} + 4 t - 12) = 0$
$5 (t + 6) (t - 2) = 0$
$t + 6 = 0$ OR $t - 2 = 0$
$t = - 6$ or $t = 2$
Since a time must be positive, discard the negative value for $t$ .