A particle is moving along a projectile path where the initial height is 160 feet with an initial speed of 144 feet per second. What is the maximum height of the particle?

128 feet
224 feet
272 feet
484 feet

Question

A particle is moving along a projectile path where the initial height is 160 feet with an initial speed of 144 feet per second. What is the maximum height of the particle? 
 	
	128 feet
	224 feet
	272 feet
	484 feet

anonymous · Answer

@iGreen

igreen · Answer

Okay, it's the same as the last one.

First, we make the equation.

$\sf H(t) = -16t^2 + vt + s$

Where 'v' is the velocity(speed) and 's' is the starting height.

igreen · Answer

So plug in 160 for 's' and 144 for 'v'..what do you get?

anonymous · Answer

$$H(t)=-16t ^{2}+144(t)+160$$

anonymous · Answer

how do we figure out t

igreen · Answer

Correct!

Now plug it into the equation $\sf\dfrac{-b}{2a}$ to find the x-value of the vertex.

igreen · Answer

$\sf H(t) = \color{red}{-16}t^2 + \color{lime}{144}t + \color{blue}{160}$

$\sf \color{red} ax^2 + \color{lime} bx + \color{blue} c$

igreen · Answer

So what are 'a' and 'b'?

anonymous · Answer

$$\frac{ -144 }{ 2(-16) }$$

anonymous · Answer

4.5 right?

anonymous · Answer

-4.5

igreen · Answer

Yep, now plug that back into the original equation for 't'.

igreen · Answer

$\sf H(t) = -16t^2 + 144t + 160$

igreen · Answer

Tell me what you get.

igreen · Answer

Oh wait, nevermind..4.5 was correct..lol.

anonymous · Answer

oh ok one sec

anonymous · Answer

$$H(t)=-16(4.5)^{2}+144(4.5)+160$$

anonymous · Answer

@iGreen  sry my connection stopped