Polynomial and Sinusoidal Funcitons

[jeje23]

A projectile launched into the air can be modelled by the function h(t) =-4.9t^(2) + 4.1t + 8.2 where h(t) represents the height of the projectile above the ground, in meters, t seconds after it was launched. What time is the projectile at a height of 3 meters?

I have it solved using quadratic formula, but just need to know if I divide my answer by 3 since it is 3t = .... thank you for the help

 

[R.M.]

You have some misunderstanding here. You do not have 3t as you stated above, you have h(t) = 3. Also, I am assuming that "I have it solved using quadratic formula" means that you solved the equation 0 = -4.9t^(2) + 4.1t + 8.2. So what you found was the height of the projectile at t = 0. Understand the meaning of this phrase: h(t) represents the height of the projectile. This means that for a particular time, h(t) is the height at that particular time. So given a height of 3 meters, i.e., h(t), find the corresponding value of t. You want to solve h(t) = 3, NOT h(t) = 0 as you originally did.

 

[HallsofIvy]

There is NO "3t" any where in this problem!

You are given that h= -4.9t^2+ 4.1t+ 8.2 and are asked when h= 3. Replacing h by 3 in the first equation, 3= -4.9t^2+ 4.1t+ 8.2.

Subtracting3 from both sides, 0= -4.9t^2+ 4.1t+ 5.2. That is the quadratic equation you want to solve.

 

[Steven G]

You have some misunderstanding here. You do not have 3t as you stated above, you have h(t) = 3. Also, I am assuming that "I have it solved using quadratic formula" means that you solved the equation 0 = -4.9t^(2) + 4.1t + 8.2. So what you found was the height of the projectile at t = 0. Understand the meaning of this phrase: h(t) represents the height of the projectile. This means that for a particular time, h(t) is the height at that particular time. So given a height of 3 meters, i.e., h(t), find the corresponding value of t. You want to solve h(t) = 3, NOT h(t) = 0 as you originally did.

Hold on here. What is in red is not true at all. Solving the quadratic equation 0 = -4.9t^(2) + 4.1t + 8.2 using any method tells you the value of t when the height is 0, not the other way around. Clearly h(0) = 8.2, not 0
You generally write excellent posts and I am glad that you are still hanging around but like everyone else here has done, you made a mistake.

 

[jeje23]

Thank you all for your responses. I understand the question much better now, and your feedback has helped me answer further similar questions.

 

[R.M.]

Hold on here. What is in red is not true at all. Solving the quadratic equation 0 = -4.9t^(2) + 4.1t + 8.2 using any method tells you the value of t when the height is 0, not the other way around. Clearly h(0) = 8.2, not 0
You generally write excellent posts and I am glad that you are still hanging around but like everyone else here has done, you made a mistake.

*smacking head* Two notes to self: don't make any more posts before caffeinating yourself in the morning, and don't click 'post' before re-reading what you just typed. Good lord was that a major blunder.....and from a 19.5 year teaching veteran no less.