Distance as function of time
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Suppose you throw a baseball straight up at a velocity of 64 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0
16 represents 1/2g, the gravitational pull due to gravity (measured in feet per second2).
v0 is the initial velocity (how hard do you throw the object, measured in feet per second).
s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.
What is the function that describes this problem?
The ball will be how high above the ground after 1 second?
How long will it take to hit the ground?
What is the maximum height of the ball? What time will the maximum height be attained?
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Solution Summary
This shows how to work with a function representing distance above ground.
Solution Preview
The general function is s(t)=-16t^2+v0t+s0.
From the condition, the initial velocity is v0=64 feet per second and you are standing on the ground, which means that s0=0. Thus the function that describes the problem ...
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