A thief is trying to escape from a parking garage after completing a robbery, and the thief's car is speeding (v = 14 m/s) toward the door of the parking garage (see figure). When the thief is L = 31 m from the door, a police officer flips a switch to close the garage door. The door starts at a height of 1.91 m and moves downward at 0.23 m/s. If the thief's car is 1.5 m tall, will the thief escape?

Question

A thief is trying to escape from a parking garage after completing a robbery, and the thief's car is speeding (v = 14 m/s) toward the door of the parking garage (see figure). When the thief is L = 31 m from the door, a police officer flips a switch to close the garage door. The door starts at a height of 1.91 m and moves downward at 0.23 m/s. If the thief's car is 1.5 m tall, will the thief escape?

Answer 1

To determine whether the thief will escape, we need to compare the time it takes for the thief to reach the door and the time it takes for the door to close.

First, let's calculate the time it takes for the thief to reach the door:
Distance = Speed × Time
31 m = 14 m/s × Time
Time = 31 m / 14 m/s
Time = 2.21 seconds

Next, let's calculate the time it takes for the door to close:
Change in Height = Speed × Time
1.91 m - 1.5 m = 0.23 m/s × Time
0.41 m = 0.23 m/s × Time
Time = 0.41 m / 0.23 m/s
Time = 1.78 seconds

Comparing the two times, we can see that the time it takes for the thief to reach the door (2.21 seconds) is greater than the time it takes for the door to close (1.78 seconds). Therefore, the thief will not be able to escape, as the door will close before the thief can reach it.