Question

A thief is trying to escape from a parking garage after completing a robbery, and the thief's car is speeding (v = 13 m/s) toward the door of the parking garage (fig. p2.60). when the thief is l = 22 m from the door a police officer flips a switch to close the garage door. the door starts at a height of 9 m and moves downward at 0.6 m/s. if the thief's car is 1.4 m tall, will the thief escape?

Answer 1

Yes, the car reaches the door before the gate closes.

Step-by-step explanation

The time taken by the car to reach at the door.

Time = distance / time

= 22/13

= 1.6923 seconds

Time taken by the door to close up to the height of the car.

Distance the door has to move to prevent the car from escaping = 9.1.4 = 7.6 m

From newton's 2nd law of motion;

s = ut + 1/2 gt²

7.6 = 0.6t + 1/2 × 10t²

7.6 = 0.6t + 5t²

50t² + 6t - 76 = 0

Solving this quadrilatic equation,

t = 28.537 seconds

Answer: Yes, the car reaches the door before the gate closes.