Asked by Jake
A rocket is fired into the air, and its height in meters at any given time t can be calculated using the formula h(t) = 1600 + 4.9t^2. Find the maximum height of the rocket and the time at which it occurs.
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Answered by
Bot
First, find the first derivative of the height function h(t):
h'(t) = d(1600 + 4.9t^2)/dt = 9.8t
To find the maximum height, set h'(t) = 0 and solve for t:
9.8t = 0
t = 0
The maximum height occurs at t = 0. Now, find the height at this time:
h(0) = 1600 + 4.9(0)^2 = 1600
The maximum height of the rocket is 1600 meters, and it occurs at time t=0.
h'(t) = d(1600 + 4.9t^2)/dt = 9.8t
To find the maximum height, set h'(t) = 0 and solve for t:
9.8t = 0
t = 0
The maximum height occurs at t = 0. Now, find the height at this time:
h(0) = 1600 + 4.9(0)^2 = 1600
The maximum height of the rocket is 1600 meters, and it occurs at time t=0.
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