A thief is trying to escape from a parking garage after completing a robbery, and the thief's car is speeding 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 2.2 m and moves downward at 0.18 m/s. If the thief's car is 1.6 m tall, what should be the minimum speed of his car to escape?

Question

A thief is trying to escape from a parking garage after completing a robbery, and the thief's car is speeding 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 2.2 m and moves downward at 0.18 m/s. If the thief's car is 1.6 m tall, what should be the minimum speed of his car to escape?

Answer 1

To determine the minimum speed of the thief's car needed to escape the parking garage, we need to consider the time it takes for the garage door to close and whether the car can clear the door before it closes.

First, let's determine the time it takes for the garage door to close. We know that the door moves downward at a rate of 0.18 m/s. Initially, the garage door has a height of 2.2 m. To find the time it takes for the door to close completely, we can use the equation:

time = distance / speed

The distance the door needs to cover is 2.2 m (initial height) minus the height of the thief's car (1.6 m). Therefore, the distance is 2.2 - 1.6 = 0.6 m.

Plugging the values into the equation, we have:

time = 0.6 m / 0.18 m/s = 3.33 seconds (rounded to two decimal places)

Now, let's analyze whether the thief's car can clear the door before it closes. We know that the thief's car is initially at a distance of 31 m from the door. We need to determine if the car can cover this distance before the door closes.

We can use the equation:

distance = speed x time

The distance the car needs to cover is 31 m, and the time available is 3.33 seconds (as calculated earlier). Rearranging the equation, we can solve for speed:

speed = distance / time

Plugging the values into the equation, we have:

speed = 31 m / 3.33 s ≈ 9.31 m/s

Therefore, the minimum speed the thief's car needs to be traveling at is approximately 9.31 m/s to escape from the parking garage.

Note: It's important to note that this calculation assumes a simplified scenario without considering factors such as acceleration or changes in speed during the car's motion.