Question
A ball is thrown into the air from a height of 7ft. The height, h, of the ball after t seconds, is given by the equation h= −4.9t^2 + 34t + 7 .
What is the maximum height the ball reaches?
Select one:
a. between 45ft and 50ft
b. between 50ft and 55ft
c. between 55ft and 60ft
d. over 60ft (is this one correct?)
What is the maximum height the ball reaches?
Select one:
a. between 45ft and 50ft
b. between 50ft and 55ft
c. between 55ft and 60ft
d. over 60ft (is this one correct?)
Answers
well I will cheat and use calculus
at to dh/dt = 0
0= -9.8 t + 34
t = 34/9.8 = 3.47 s
so
h= −4.9(3.47)^2 + 34(3.47) + 7
= -59 + 118 +7
= 66
so yes
at to dh/dt = 0
0= -9.8 t + 34
t = 34/9.8 = 3.47 s
so
h= −4.9(3.47)^2 + 34(3.47) + 7
= -59 + 118 +7
= 66
so yes
h= −4.9t^2 + 34t + 7
parabola look for vertex
4.9 t^2 -34 t = -h + 7
t^2 - 6.94 t = -h/4.9 + 1.43
t^2 - 6.94 t + 12.0 = -h/4.9+ 13.43
(t-3.47)^2 = -h/4.9+ 65.8/4.9 = -(1/4.9)(h-65.8)
so t = 3.47 and h = 65.8 at vertex
parabola look for vertex
4.9 t^2 -34 t = -h + 7
t^2 - 6.94 t = -h/4.9 + 1.43
t^2 - 6.94 t + 12.0 = -h/4.9+ 13.43
(t-3.47)^2 = -h/4.9+ 65.8/4.9 = -(1/4.9)(h-65.8)
so t = 3.47 and h = 65.8 at vertex
−4.9t^2 + 34t + 7
the vertex is at t = -b/2a = 34/9.8
the height is h = c - b^2/4a = 7 + 34^2/19.6
the vertex is at t = -b/2a = 34/9.8
the height is h = c - b^2/4a = 7 + 34^2/19.6
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