A 10.0-m-long truck moving with a constant velocity of 97.0 km / h passes a 3.0 -m-long car movi

step 1 This problem is interesting. It's a relative velocity problem. You're told you have a truck. So

A 10.0-m-long truck moving with a constant velocity of 97.0...

A 10.0-m-long truck moving with a constant velocity of $97.0 \mathrm{km} / \mathrm{h}$ passes a 3.0 -m-long car moving with a constant velocity of $80.0 \mathrm{km} / \mathrm{h}$. How much time elapses between the moment the front of the truck is even with the back of the car and the moment the back of the truck is even with the front of the car?

Key Concepts

Relative Speed

Relative speed is the difference in velocities of two moving objects when they are traveling in the same direction. It represents how fast one object is approaching or receding from the other. Using relative speed simplifies the problem by reducing it to a single effective speed, which is then used to determine the time required for one object to cover the relative distance necessary to complete an overtaking maneuver.

Relative Distance

Relative distance in the context of overtaking problems refers to the total distance that needs to be covered for one vehicle to completely pass another. This distance typically includes the entire length of the vehicle that is overtaking and the entire length of the vehicle being overtaken. Understanding how to combine these lengths correctly is critical to determining the precise moment when the overtaking event is complete.

Relative Motion

This concept involves analyzing the motion of one object from the viewpoint of another moving object. Instead of considering each object's individual velocity relative to the ground, the problem is simplified by subtracting one velocity from the other to evaluate their motion with respect to each other. It is especially useful in scenarios where both objects are moving along the same path or direction, as it allows one to determine how quickly one object overtakes the other.

Unit Conversion

In many physics problems, speeds and distances must be in consistent units for accurate calculations. When speeds are given in kilometers per hour (km/h) but distances are required in meters (m), converting km/h to m/s is essential. This conversion is performed by multiplying the km/h value by a factor that adjusts for the difference between kilometers and meters as well as hours and seconds.

Transcript

00:01 This problem is interesting.

00:02 It's a relative velocity problem.

00:04 You're told you have a truck.

00:06 So the length of the truck is given as 10 meters and it's moving with the velocity of the truck of 97 kilometers per hour.

00:16 You should right away convert that to meters per second, which is 26 .94 meters per second.

00:23 A thousand meters in a kilometer, 3 ,600 seconds in an hour.

00:27 You use those two qualities to solve and get that velocity.

00:30 You also have the length of the car, which is said to be three meters.

00:34 The velocity of the car is given as 80 kilometers per hour.

00:39 Likewise, you have to convert that, and you get 22 .22 meters per second.

00:46 So both moving in the same direction.

00:47 It says, how long does it take the truck to pass the car? so what you have to do is find the velocity of the truck with respect to the car.

00:54 So i'm going to write a relative motion equation.

00:57 Velocity of the truck with respect to the ground, plus the velocity, of the ground with respect to the car is equal to the velocity of the truck with respect to the car.

01:11 So if you put all things, i know the velocity of the truck with respect to the ground.

01:15 That's 26 .94 to the right...

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