A thief is trying to escape from a parking garage after completing a robbery, and the thief’s car is speeding (v = 17.5 m/s) toward the door of the parking garage. When the thief is L = 14 m from the door a police officer flips a switch to close the garage door. The door starts at a height of 6.5 m and moves downward at 0.1 m/s. If the thief’s car is 1.4 m tall, will the thief escape? (Find the height of the door above the ground).
yes
hf=hi+vi*t
1.4=6.5 -.1t
solve for time t.
is this less than the time for the policemand to get there?
timepolice= 14/17.5 seconds
5.1
To determine if the thief will escape, we need to find the height of the door above the ground when the thief reaches it.
We can begin by calculating the time it will take for the thief to reach the door. We can use the equation:
time = distance / velocity
In this case, the distance is given as L = 14 m and the velocity as v = 17.5 m/s, so we have:
time = 14 m / 17.5 m/s
Performing the calculation, we find:
time = 0.8 s
Next, we need to calculate how far the garage door has moved downwards during this time. We can use the equation:
distance = velocity * time
Here, the velocity is given as -0.1 m/s (negative due to the downward motion) and the time as 0.8 s, so we have:
distance = -0.1 m/s * 0.8 s
Performing the calculation:
distance = -0.08 m
Since we are interested in the height of the garage door above the ground, we need to determine the final position of the door. The initial height of the door is given as 6.5 m, and it has moved -0.08 m down. Therefore, the final height of the door is:
final height = initial height - distance moved
final height = 6.5 m - (-0.08 m)
Simplifying the calculation:
final height = 6.5 m + 0.08 m
final height = 6.58 m
Finally, to determine if the thief will escape, we compare the final height of the door with the height of the thief's car. If the final height is greater than the height of the thief's car, the thief will escape. In this case, the thief's car is 1.4 m tall and the final height of the door is 6.58 m, so we have:
6.58 m > 1.4 m
Since the final height of the door is greater than the height of the thief's car, we can conclude that the thief will escape.