Answer:
a) -13.9 ft/s
b) 13.9 ft/s
Step-by-step explanation:
a) The rate of his distance from the second base when he is halfway to first base can be found by differentiating the following Pythagorean theorem equation respect t:
(1)
(2)
Since:
When x = 45 (the batter is halfway to first base), D is:
Now, by introducing D = 100.62, x = 45 and dx/dt = 31 into equation (2) we have:
Hence, the rate of his distance from second base decreasing when he is halfway to first base is -13.9 ft/s.
b) The rate of his distance from third base increasing at the same moment is given by differentiating the folowing Pythagorean theorem equation respect t:
(3)
We have that D is:
By entering x = 45, dx/dt = 31 and D = 100.63 into equation (3) we have:
Therefore, the rate of the batter when he is from third base increasing at the same moment is 13.9 ft/s.
I hope it helps you!