Final answer:
To find the total time an arrow spends in the air (ta), we can use the equation ta = 2v0/g, assuming the arrow lands at the same height it was launched and the only force acting on it is gravity.
Step-by-step explanation:
To determine the time an arrow spends in the air (ta), with a known initial velocity (v0) and assuming that the only force acting on it is gravity (g), we can use the kinematic equation for uniformly accelerated motion:
v = v0 + at
Since we are considering the motion of an arrow being launched and then landing (assuming it lands at the same height it was launched), the final velocity (v) at the peak of its flight for vertical motion is 0 m/s, and the acceleration (a) is the acceleration due to gravity (g), which is approximately 9.81 m/s2 downward, hence 'a' becomes '-g'.
Plugging in the known values and rearranging the equation to solve for time (t), we get:
0 = v0 - g*t
t = v0/g
This represents the time for the arrow to reach the maximum height. However, the total time spent in the air will be twice this as it has to come back down. Therefore, the total time the arrow spends in the air (ta) is calculated as:
ta = (2 * v0/g)
Thus, the correct answer is (b) ta = 2v0/g.