Find the average velocity of the ball over the time interval from 4 to 4+h seconds when h cant = 0? When a ball is thrown vertically upwardinto the air with a velocity of 67 ft/sec itsheight,...
When a ball is thrown vertically upward
into the air with a velocity of 67 ft/sec its
height, y(t), in feet after t seconds is given by
y(t) = 67t − 16t^2 .
By definition, the average velocity on the time interval `[t_1,t_2]` is
`(y(t_2)-y(t_1))/(t_2-t_1)` . In this case, we are given that `t_1=4` seconds and `t_2=4+h` seconds. We plug these into the given equation to get
`y(4)=67*4-16*4^2=268-256=12` feet and
`=-16h^2-61h+12` feet. Now we just plug these into the average velocity formula:
The units in the numerator are feet and the units in the denominator are seconds, so the units of velocity turn out to be feet/second, as expected. The reason h can't be 0 is to avoid division by zero.
The average velocity on the interval [4,4+h] is -16h-61 ft/s.
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