Question
A projectile is thrown upward with an initial velocity of 272 feet per second. After t seconds, its height h(t)above the ground is given by the function : h(t)=-16t^2+272t.
a. Determine the projectile's maximum height.
b. Determine how long it takes the projectile to reach its maximum height.
c. How many seconds will it take the projectile to strike the ground after it is thrown?
a. Determine the projectile's maximum height.
b. Determine how long it takes the projectile to reach its maximum height.
c. How many seconds will it take the projectile to strike the ground after it is thrown?
Answers
Reiny
Since you called it "College Algebra" I will assume you know Calculus.
h'(t) = -32t + 272
b) max height obtained when
-32t+272 = 0
t = 8.5 seconds
a) h(2.5) = -16(8.5)^2 + 272(8.5) = 1156
c) to strike ground, h(t) = 0
-16t^2 + 272t = 0
-16t(t - 17) = 0
t = 0, (at the start) or t = 17
It will hit the ground 17 seconds later.
h'(t) = -32t + 272
b) max height obtained when
-32t+272 = 0
t = 8.5 seconds
a) h(2.5) = -16(8.5)^2 + 272(8.5) = 1156
c) to strike ground, h(t) = 0
-16t^2 + 272t = 0
-16t(t - 17) = 0
t = 0, (at the start) or t = 17
It will hit the ground 17 seconds later.