I'm wonder if im correct?
Two physics students built a model rocket for a class project. Once the rocket is launched, its height in feet, h(t), can be found using the height function
h(t) = -16t² + 96t where t represents time in seconds
my work: 0=-16t^2+96t = -16t(t-6)=0 = -16t=0 , t=0 and t-6= t=6.
Is this correct?
I wonder what the problem is.
Question:
Two physics students built a model rocket for a class project. Once the rocket is launched, its height in feet, h(t), can be found using the height function
h(t) = -16t² + 96t where t represents time in seconds.Find the time when the rocket finally hits the ground.
LOL, well if 6 is the answer then
-16(36) + 96 (6) better be zero
is it ? :)
where is the 36 from?
Your work is almost correct, but there is a little mistake in your calculations.
The equation is given by: h(t) = -16t^2 + 96t.
To find the values of t that make h(t) equal to zero (since that would represent the rocket hitting the ground), you need to solve the equation:
-16t^2 + 96t = 0.
To start, you can factor out a common factor of -16 from both terms:
-16t(t - 6) = 0.
Now, you have two factors: -16t and (t - 6). For the equation to be equal to zero, either -16t = 0 or (t - 6) = 0.
Solving for -16t = 0, you divide both sides by -16, giving you t = 0.
Solving for (t - 6) = 0, you add 6 to both sides, giving you t = 6.
So, the values of t that make h(t) equal to zero are t = 0 and t = 6.
Therefore, your mistake was when you wrote "-16t = 0, t = 0 and t - 6 = t = 6." It should have been "-16t = 0, t = 0 and t - 6 = 0, t = 6."
Overall, your reasoning was correct; however, I hope this explanation helps you understand the process better.