Question

A projectile is launched from a point above the ground. The height at ground level is given by the equation h = -3t² + 24t, where H is the height in meters and T is the time in seconds.

A. What is the maximum height it can be reach?
B. How long will it take to reach the maximum height?

Pls show the complete solution and answer.

Answer 1

Ok so given the equation we know that h is meters and t is time in seconds

Answer 2

given this quadratic h(t) = -3t^2 +24t

hope you know that a quadratic a graph of parabola

a. to get the max height you need calcule the max point of this parabola
b. so for this you just need check it for what value of t will get the max point of this parabola

hope helped understandably easy

Answer 3

Ok to find the time that the projectile is in maximum height we can do

dh/dt=0

d/dt(-3t^2+24t)=0

d/dt(-3t^2) +d/dt(24t)=0

-6t+24=0

-6t=24

t=4

4 seconds will be the time the projectile is a maximum height

Answer 4

@Pimalea do you understand these above wrote calcule ?

Answer 5

Thank you very much for the help, justus and jhonny 9,all your help is very much appreciated.

Answer 6

Now we can use the 4 seconds in the equation

-3x(4)^2+24 x 4

-3 x 16 + 96

-48 + 96 = 48

48 meters is the maximum height it reacts after 4 seconds of launch

Answer 7

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Pimalea
Thank you very much for the help, justus and jhonny 9,all your help is very much appreciated.
\(\color{#0cbb34}{\text{End of Quote}}\)
My pleasure.