When Will the Object Be 15 Meters Above the Ground?

[karush]

$\tiny{1.2.1}$
An object is propelled vertically upward with an initial velocity of 20 meters per second.
The distance s (in meters) of the object from the ground after t seconds is
$s=-4.9t^2+20t$
(a) When will the object be 15 meters above the ground?
$15=-4.9t^2+20 \implies -4.9t^2 =-5$
ok there is no term b so decided not to use quadratic formula
so far...:unsure:
$49t^2=50$

(b) When will it strike the ground?
(c) Will the object reach a height of 100 meters

 

[topsquark]

$\tiny{1.2.1}$
An object is propelled vertically upward with an initial velocity of 20 meters per second.
The distance s (in meters) of the object from the ground after t seconds is
$s=-4.9t^2+20t$
(a) When will the object be 15 meters above the ground?
$15=-4.9t^2+20 \implies -4.9t^2 =-5$
ok there is no term b so decided not to use quadratic formula

You dropped the t on the 20t term in going from \(\displaystyle s = -4.9t^2 + 20t\) to \(\displaystyle 15 = -4.9t^2 + 20t\).

-Dan

 

[karush]

.

 

[karush]

You dropped the t on the 20t term in going from \(\displaystyle s = -4.9t^2 + 20t\) to \(\displaystyle 15 = -4.9t^2 + 20t\).

-Dan

$15 = -4.9t^2 + 20t
\implies 4.9t^2-20t+15=0
\implies 49t^2-200t+150=0$
kinda hefty for a quadratic equation so went to W|A
$t\approx 3.0914s$ probably this since it is going up
$t\approx 0.99024s $

it was tempting to just round off the 4.9 but think this how fast things fall

 

[topsquark]

$15 = -4.9t^2 + 20t
\implies 4.9t^2-20t+15=0
\implies 49t^2-200t+150=0$
kinda hefty for a quadratic equation so went to W|A
$t\approx 3.0914s$ probably this since it is going up
$t\approx 0.99024s $

it was tempting to just round off the 4.9 but think this how fast things fall

Mostly a good job. On the way up it passes 15 m at t = 0.099024 s. g is the acceleration due to gravity so it's how fast it is changing how fast it is falling. (Just call it an acceleration.. it's easier!)

Technically g is about 9.81 m/s^2 but the number locally is slightly different everywhere so it changes a bit. 9.8 m/s^2 is good enough.

-Dan