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Sagot :
Answer:
64 m, at time t = 4 sec
Step-by-step explanation:
We must maximize the function h = 32t – 4t^2. One way in which to do this is to find the axis of symmetry, t = -b / [2a], and from that calculate the height:
a = -4, b = 32, c = 0
-32
and therefore the axis of symmetry is t = ---------------- = 4
2(-4)
The height, h, at time t = 4, is h(4) = 32(4) - 4(4)^2 = 64 m
The maximum height of the ball is 64 m, at time t = 4 sec
Step-by-step explanation:
The golf ball reaches its maximum vertical height when its vertical velocity h' becomes zero. Taking the derivative of h and setting it to zero, we get
h' = 32 - 8t = 0
which gives us t = 4 seconds. So after 4 seconds, the ball will reach its maximum height and its value is
h = 32(4) - 4(4)^2
= 128 - 64
= 64
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