Question

Elijah was analyzing the trajectory made after throwing a football. His coach was able to measure that his throw reached a maximum height of 16 feet after 2 seconds. He figured that the ball left his hand at a height of 4 feet. Let the independent variable represent time and the dependent variable represent height of the ball. Use this information to write an equation to model the path of the ball and predict when the ball will hit the ground.

Answer 1

Explanation:

Given that Elijah threw a ball from a height of 4 feet. The ball reached maximum height of 16 feet after 2seconds

Let vertical component of his speed be v

When it reaches maximum height its velocity becomes 0

Hence

height reached by the ball =
`h=vt-(gt^2)/(2)`

When h=12(16-4) we get g=gravity =32

Hence 12 =2v-16(4)

v=38

Hence
`h=38t-(32t^2)/(2)`

where h is calculated from the height of hand i.e. 4 feet

When it touches the ground h =-4

When it starts falling then distance travelled = 16 feet

Initial velocity =0 Accn due to gracity =32 feet

Using these we can write

`16=0+(32t^2)/(2)\\ t=1`

So after 3 minutes from start the ball would reach the ground