science fair drop

Question

For a science competition, students must design a container that prevents an egg from breaking when dropped from a height of 50​ feet. The function h=-16t^2+50 gives the height in feet of the container after t seconds and the container will fall for about 1.8 seconds before it hits the ground. The students find that h(1)- h(1.5) =20 So, the container fell 20 feet between 1​ and 1.5 seconds.

Next, the egg container is dropped from a height of 80 feet.

a. Write a function that gives the height h  (in feet) of the container after t​  seconds. How long does the container take to hit the ground? Round to the nearest tenth, if necessary.

Answer 1

The height of an object in free fall is given by the formula:

height = initial height - (1/2) x gravity x time^2

For the egg dropped from 50 feet, the equation is:

h = 50 - 16t^2

For an egg dropped from 80 feet, the equation will be:

h = 80 - 16t^2

To find out how long it takes for the egg container to hit the ground, we set the height to 0:

0 = 80 - 16t^2

Solving for t^2, we get:

t^2 = 5

Taking the square root of both sides, we get:

t = 2.24

So, when dropped from 80 feet, the container will take about 2.2 seconds to hit the ground.

Hope this helps 🙂

Answer 2

h = -16t² + 80

0 = -16t² + 80

Can you solve for t and answer?