Solving Applications Involving Quadratic Models

[NoGoodAtMath]

A bad punter on a football team kicks a football approximately straight upward with an initial velocity of 75 fy/sec.
a) If the ball leaves his foot from a height of 4 ft, write an equation for the vertical height s(in feet) of the ball t seconds after being kicked.

I wrote the model and it's -16t^2+75t+4

My problem is the second part.

b). Find the time(s) at which the ball is at a height of 80 ft. Round to 1 decimal place.

 

[wjm11]

A bad punter on a football team kicks a football approximately straight upward with an initial velocity of 75 fy/sec.
a) If the ball leaves his foot from a height of 4 ft, write an equation for the vertical height s(in feet) of the ball t seconds after being kicked.

I wrote the model and it's -16t^2+75t+4

My problem is the second part.

b). Find the time(s) at which the ball is at a height of 80 ft. Round to 1 decimal place.

Notice that the instructions said to write an equation. So far you have only written an expression. You don't have a "something" = "something". You need to write:

h = -16t^2 + 75t + 4

where h is the height and t is the time. Now simply substitute in the height you are interested in, h = 80, and solve for t:

80 = -16t^2 + 75t + 4

What methods do you know for solving a quadratic equation? The quadratic formula is always handy.

 

[Ishuda]

A bad punter on a football team kicks a football approximately straight upward with an initial velocity of 75 fy/sec.
a) If the ball leaves his foot from a height of 4 ft, write an equation for the vertical height s(in feet) of the ball t seconds after being kicked.

I wrote the model and it's -16t^2+75t+4

My problem is the second part.

b). Find the time(s) at which the ball is at a height of 80 ft. Round to 1 decimal place.

Assuming the ball reaches a height greater than 80 feet, it will reach a height of 80 feet twice, once on the way up and once on the way down. Since you have a formula for the height
s(t) = -16 t² + 75 t + 4
you want to solve the equation
s(t) = 80
or
-16 t² + 75 t + 4 = 80

Note that the way the problem is given, the solution requires an assumption that the initial vertical velocity is 75 ft/sec. In that case, it really doesn't matter whether the punter was bad or good, the time would be the same for either (assuming no air resistance, etc.). That 'bad punter' part seems to imply that the 'vertical' is to be understood and the 'approximately straight upward' is so close to straight up that the difference wouldn't make any difference in the first decimal place. Oh, and at least the bad punter has a good hang time

 

[NoGoodAtMath]

Solving Appications Involving Quadratic Models

Notice that the in your instructions said to write an equation. So far you have only written an expression. You don't have a "something" = "something". You need to write:

h = -16t^2 + 75t + 4

where h is the height and t is the time. Now simply substitute in the height you are interested in, h = 80, and solve for t:

80 = -16t^2 + 75t + 4

What methods do you know for solving a quadratic equation? The quadratic formula is always handy.

I know the quadratic formula. I guess ill use that instead. Thanks, I should get this problem solved.