Mathematics: Sandra throws an object straight up into the air with initial velocity of 38 ft per square from platform that is 30 ft above the ground how long will it take for object to hit the ground

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Sandra throws an object straight up into the air

Ответ:

jothianddeepi

19.01.2022

Mathematics

3 seconds.

Step-by-step explanation:

We have been given that Sandra throws an object straight up into the air with initial velocity of 38 ft per second from platform that is 30 ft above the ground.

To find the time it will take for object to hit the ground, we will use formula:

h(t)=-16t^2+v_0t+h_0 , where, v_0 represents initial velocity and h_0 represents initial height.

Upon substituting our given initial velocity and initial height, we will get:

h(t)=-16t^2+38t+30

We know that object will hit the ground, when height will be 0, so we will equate object's height equal to 0 and solve for t as:

-16t^2+38t+30=0

Divide by 2:

-8t^2+19t+15=0

Upon using quadratic formula, we will get:

$t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-19\pm\sqrt{19^2-4(-8)(15)}}{2(-8)}$

$t=\frac{-19\pm\sqrt{361+480}}{-16}=\frac{-19\pm\sqrt{841}}{-16}$

$t=\frac{-19\pm29}{-16}$

$t=\frac{-19-29}{-16},t=\frac{-19+29}{-16}$

$t=\frac{-48}{-16},t=\frac{10}{-16}$

$t=3,t=-\frac{5}{8}$

Since time cannot be negative, therefore, it will take 3 seconds for object to hit the ground.

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Sandra throws an object straight up into the air with initial velocity of 38 ft per square from platform that is 30 ft above the ground how long will it take for object to hit the ground

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