# When Will the Object Be 15 Meters Above the Ground?

• MHB
• karush
In summary: 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!)-Dan
karush
Gold Member
MHB
$\tiny{1.2.1}$
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

karush said:
$\tiny{1.2.1}$
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

.

Last edited:
topsquark said:
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

karush said:
$15 = -4.9t^2 + 20t \implies 4.9t^2-20t+15=0 \implies 49t^2-200t+150=0$
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

## What is the initial velocity of the object?

The initial velocity of the object is 20 meters per second.

## What is the acceleration of the object?

The acceleration of the object is -9.8 meters per second squared, due to the force of gravity pulling the object down.

## What is the maximum height reached by the object?

The maximum height reached by the object can be calculated using the formula h = (v^2)/(2g), where v is the initial velocity and g is the acceleration due to gravity. In this case, the maximum height would be approximately 20.41 meters.

## How long does it take for the object to reach its maximum height?

The time it takes for the object to reach its maximum height can be calculated using the formula t = v/g, where v is the initial velocity and g is the acceleration due to gravity. In this case, it would take approximately 2.04 seconds for the object to reach its maximum height.

## What is the velocity of the object at its maximum height?

The velocity of the object at its maximum height is 0 meters per second, as the object has reached its highest point and is about to start falling back down due to gravity.

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