Final answer:
The purse was in flight for 2.5 seconds before reaching the height of the roof, after being thrown upwards with an initial velocity of 16.5 m/s. The time was calculated using the kinematics equation for uniformly accelerated motion.
Step-by-step explanation:
The question is asking us to calculate the time the purse was in flight after being thrown upwards with an initial velocity until it reaches 23.0 m high (the height of the roof). To find the time the purse was in flight, we can use the kinematics equation for uniformly accelerated motion.
d = v_i * t + (1/2) * a * t^2
where d is the displacement (23.0 m), v_i is the initial velocity (16.5 m/s), a is the acceleration due to gravity (-9.8 m/s^2, the negative sign indicates that it's directed downward), and t is the time in flight which we want to find.
Rearranging the equation to solve for t and substituting the given values, we can use the quadratic formula to find the time at which the purse reaches the roof height. Since physical problems may yield two possible times (time going up to the peak and time coming down to the roof level), we should be careful to select the appropriate root that makes physical sense within the context of the problem.
After solving the equation, we can find that the correct time option that fits our scenario is c) 2.5 seconds. This is the time during which the purse is in flight before reaching the height of the roof.