Question

A particle is moving along a projectile path at an initial height of 160 feet with an initial speed of 144 feet per second. This can be represented by the function H(t) = −16t2 + 144t + 160. What is the maximum height of the particle?

Answer 1

Answer:

The maximum height of the particle is 484 m.

Step-by-step explanation:

Given that,

A particle is moving along a projectile path at an initial height of 160 feet with an initial speed of 144 feet per second. This can be represented by the function :

$H(t) = -16t^2 + 144t + 160$ ....(1)

We need to find the maximum height of the particle. For maximum height put $\dfrac{dH}{dt}=0$

So,

$\dfrac{d(-16t^2+144t+160)}{dt}=0\\\\-32t+144=0\\\\t=4.5\ s$

Put t = 4.5 s in equation (1) as :

$H(t) = -16(4.5)^2 + 144(4.5)+ 160\\\\H(t)=484\ m$

So, the maximum height of the particle is 484 m.