Question

Solve using the best method:

A football is punted into the air. Its height

h, in meters, after t seconds is given by the

equation h = -4.912 + 24.5t + 1. When

does the ball hit the ground?

Answer 1

Answer: After 5.02 seconds

Explanation:

The correct equation in the question is h= -4.912 t²+ 24.5t + 1

Hi, when the ball hits the ground, height =0.

So, replacing in the equation:

0= -4.912 t²+ 24.5t + 1

For: ax2+ bx + c

x =[ -b ± √b²-4ac] /2a (quadratic formula)

Replacing with the values given:

x =[ -24.5 ± √24.5²-4(-4.912)1] /2(-4.912)

x = [ -24.5 ± √600.25+19.648] /-9.824

x = [ -24.5 ± √619.898] /-9.824

x = [ -24.5 ± 24.90] /-9.824

Positive:

x = [ -24.5 +24.90 ] /-9.824 = -0.04 seconds

Negative:

x = [ -24.5 -24.90] /-9.824 = 5.02 seconds

Since time can't be negative, the answer is 5.02 seconds.

Feel free to ask for more if needed or if you did not understand something.

Answer 2

Explanation:

Question not written well

The equation of the ball is meant to be in a parabola or trajectory form.

So, h = -4.912t² + 24.5t + 1

The ball will hit the ground when the height is 0

I.e. h= 0

Therefore,

-4.912t² + 24.5t + 1 = 0

Using almighty formula,

a = -4.912 b = 24.5 c = 1

t = (-b±√b²-4ac) / 2a

t = (-24.5±√24.5²-4×-4.912 × 1) / 2 × -4.912

t = (-24.5±√600.25 + 19.648) / 9.824.

t = (-24.5 ± 24.898) / 9.824

So,

t = (-24.5 + 24.898) / 9.824

t = 0.398 / 9.824

t = 0.04seconds

Or

t = (-24.5 - 24.898) / 9.824

t = -5.03 seconds

So, we are going to discard the negative time,

t = 0.04 second is the correct time the ball will hit the ground