A T-ball player hits a ball from a tee that is 0.6m tall. The height of the ball at a given time is modelled by the function `h(t)=-4.9t^2+7t+0.6` .where height, h(t) is in metres and time, t, is...

A T-ball player hits a ball from a tee that is 0.6m tall. The height of the ball at a given time is modelled by the function `h(t)=-4.9t^2+7t+0.6` .

where height, h(t) is in metres and time, t, is in seconds.

A) What will the height be after 1s?

b) When will the ball hit the ground?

Expert Answers
hala718 eNotes educator| Certified Educator

`h(t)= -4.9t^2 + 7t +0.6`

`` a) we need to find the height of the ball after t= 1 second.

We will substitute with t= 1.

==> h(1)= -4.9(1) + 7(1)+ 0.6 = 2.7 m

Then the height after 1 second is 2.7 meters.

 

b)When will the ball hit the ground.

When the ball hit the ground then the height h= 0.

==> `h(t)= -4.9t^2 + 7t + 0.6 = 0 `

`==gt -4.9t^2 + 7t + 0.6 = 0`

Now we will solve for t.

==>`t1= (-7+sqrt(49+4*0.6*4.9))/(2*-4.9) = (-7+7.7949)/(-9.8)= -0.0811 ( Not valid) `

`==gt t2= (-7-7.7974)/(-9.8) = 1.9143` seconds.

Then the time for the ball to hit the ground is 1.9143 seconds.