Question

The function of f(x)=8√x gives the speed in feet per second (ft/s) of a free falling object after it has fallen x feet (ignoring air resistance). Find the speed of the object after it has fallen 48 feet. If necessary, round your answer to the nearest tenth.
a. 19.6 ft/s
b. 6.9 ft/s
c. 55.4 ft/s
d. 384 ft/s

Answer 1

Answer:

c. 55.4 ft/s

Step-by-step explanation:

Speed of the object is represented by the function:

$f(x)=8\sqrt{x}$

where x represents the number of feet the object has fallen. We have to find the speed of the object after it has fallen 48 feet. This means we have to find f(x) for x = 48. Substituting x = 48 in above equation we get:

$f(48)=8\sqrt{48}\\\\ =8\sqrt{16 \times 3}\\\\ =8\sqrt{4^{2} \times 3}\\\\ = 8 \times 4 \sqrt{3}\\\\ =32\sqrt{3}\\\\ = 32 \times 1.732\\\\ = 55.4$

Thus, rounded to nearest tenth, the speed of the object after it has fallen 48 feet would be 55.4 ft/s