To find the maximum height of the rocket, we need to first find the time it takes for the rocket to reach its maximum height.
At the maximum height, the velocity of the rocket is 0. So, we can set the velocity function as v(t) = -9.8t + 19.6 equal to 0 and solve for t:
-9.8t + 19.6 = 0
-9.8t = -19.6
t = 2 seconds
Now that we have the time it takes for the rocket to reach its maximum height, we can plug this value into the height function:
h(2) = 1/2(-9.8)(2)^2 + 19.6(2) + 0.5
h(2) = -19.6 + 39.2 + 0.5
h(2) = 19.1 meters
Therefore, the toy rocket is approximately 19.1 meters above the ground when it explodes.
A toy rocket is shot upward into the air from a height of 1/2 meter above the ground with an initial velocity of 19.6 meters per second. The formula for the vertical motion of an object is h(t)=1/2at^2+vt+s, where , where the gravitational constant ,a is -9.8 meters per second squared, v is the initial velocity, s is the initial height, and h (t) is the height in meters modeled as a function of time, t
Due to a malfunction, the toy rocket explodes when it reaches its maximum height. How high above the ground is the toy rocket when it explodes? Round to the nearest tenth.
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