plssssss help fast!!!!Launching From a Tower
Suppose a projectile is launched from a tower into the air with an initial velocity of 48 feet per
second. Its height, h, in feet, above the ground is modeled by the function
h = -16t2 + vot + 64
where t is the time, in second, since the projectile was launched and v, is the initial velocity.
A. What tower platform height was the projectile launched from?
B. How long was the projectile in the air?
C. When did it reach its maximum height?
D. What was its maximum height?
E. What domain makes sense for the function in this context?
Answers
Answer:
A. h = 64
B. t = 4 -> 4 seconds
C. t = 1.5 -> 1.5 seconds
D. maximum height is 100 ft
E. The domain that makes sense for the function in this context is t
is any positive real number since time can not be negative.
Step-by-step explanation:
h = -16t2 + vt + 64
A. What tower platform height was the projectile launched from?
when the projectile was not launched, t = 0
h = -16(0)^2 + v(0) + 64 = 64
B. How long was the projectile in the air?
if the projectile lands, its height = 0 so substitute 0 for h
0 = -16(t)^2 + 48(t) + 64
= -16(t^2 - 3t - 4)
= -16(t - 4)(t + 1)
t = 4 or t = -1
Since time can not be negative, t = -1 can not be the answer. Therefore, the projectile lands when t = 4 or 4 seconds.
C. When did it reach its maximum height?
maximum -> t=-b/2a where in -16(t)^2 + 48(t) + 64, b = 48 and a = -16
t = -48/-32 = 1.5
D. What was its maximum height?
plug t = 1.5 into -16(t)^2 + 48(t) + 64
-16(1.5)^2 + 48(1.5) + 64 = -36 + 72 + 64 = 100
E. The domain that makes sense for the function in this context is t
is any positive real number since time can not be negative.
The maximum height is 100 feet at a time of about 1.5 seconds.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given that:
h = -16t² + vt + 64
-16t² + 48t + 64 = h
h is the height, v is the initial velocity and t is the time.
a) The tower height is about 64 feet from the equation
b) The time is at h = 0, hence:
-16t² + 48t + 64 = 0
t = 4 seconds
c) Maximum height is at h' = 0
h' = -32t + 48
-32t + 48 = 0
t = 1.5 seconds
d) h(1.5) = -16(1.5)² + 48(1.5) + 64 = 100 feet
Find out more on equation at: https://brainly.com/question/1214333
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