A projectile that is fired vertically into the air with an initial velocity
of 120 ft. per second can be modeled by the equation s = 1200 -
16t, where s is the distance in feet of the projectile above the
ground after t seconds.
answer in step by step please
Answers
Given : A projectile that is fired vertically into the air with an initial velocity
of 120 ft. per second can be modeled by the equation s = 120t - 16t²
To Find : The question is How long will it take for a projectile to reach 216 feet?
and is it possible for the projectile to reach 900 feet?
Solution:
s = 120t - 16t²
to reach 216 feet
=> 120t - 16t² = 216
=> 16t² - 120t + 216 = 0
=> 2t² - 15t + 27 = 0
=> 2t² - 6t - 9t + 27 = 0
=> 2t(t - 3) - 9(t - 3) = 0
=> (2t - 9) (t - 3) = 0
=> t = 9/2 , t = 3
it will take 3 sec and 9/2 sec to reach 216 feet
s = 120t - 16t²
=> ds/st = 120 - 32t
=> t = 120/32 = 15/4
d²s/dt² = - 32 < 0
Hence maximum height at t = 15/4
s = 120t - 16t²
s = 120(15/4) - 16(15/4)²
= 450 - 225
= 225
225 feet is the max height
Learn More:
The minimum and maximum velocities of an oblique projectile are ...
https://brainly.in/question/11728558
A Projectile Is Thrown With Speed U Making Angle Theta With ...
https://brainly.in/question/11072190