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Chapter 2: Problem 55

A truck tractor pulls two trailers, one behind the other, at a constant speed of \(100 \mathrm{~km} / \mathrm{h}\). It takes \(0.600 \mathrm{~s}\) for the big rig to completely pass onto a bridge \(400 \mathrm{~m}\) long. For what duration of time is all or part of the trucktrailer combination on the bridge?

Short Answer

Expert verified
The duration time the truck-trailer combination is on the bridge is 15.000 seconds.

Step by step solution

01

Convert speed to m/s

First convert the speed from kilometers per hour to meters per second, since the other given measurements are in meters and seconds. The conversion rate is 1 km/hr equals \( 0.27778 \) m/s. Therefore, the speed of the truck is \( 100 \) km/hr \( \times 0.27778 \mathrm{~m/\mathrm{s}}/\mathrm{km/\mathrm{h}} = 27.778 \mathrm{~m/\mathrm{s}} \).
02

Calculate the time it takes the truck to cross the bridge

Next, calculate the time it takes for the truck to cross the bridge only. Using the formula: \( time = distance/speed \), this calculation will be \( 400 \mathrm{~m} / 27.778 \mathrm{~m/\mathrm{s}} = 14.400 \mathrm{~s} \).
03

Calculate the total time

Finally, add the time it takes for the truck to cross the bridge (found in step 2) to the time it takes the tractor to leave the bridge (given in the problem as 0.600 s). Therefore, the total time is \( 14.400 \mathrm{~s} + 0.600 \mathrm{~s} = 15.000 \mathrm{~s} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Kinematics in Motion
Kinematics is a branch of physics that deals with the principles of motion without considering its causes. In this exercise, we focus on understanding how to analyze the motion of the truck and trailers as they cross the bridge. When solving problems in kinematics, it is crucial to identify the parameters like speed, distance, and time, as they help in determining how an object moves.
To comprehend kinematics effectively:
  • Recognize the type of motion: Is it uniform or accelerated? In the given exercise, the truck and trailers are moving at a constant speed, indicating uniform motion.
  • Understand the relationship between the key variables: Speed is how fast an object is moving, distance is how far it travels, and time is the duration of the motion.
Kinematics allows us to break down complex motion into manageable calculations, making it easier to understand how objects behave when moving through space.
Speed Conversion Techniques
Converting speed from one unit to another is a common task in physics. It's essential, especially when dealing with international systems of units where different standards can be used. In our solution, converting the truck's speed from kilometers per hour (km/h) to meters per second (m/s) is necessary. This step ensures consistency with the other units provided in the problem.
Here's a simple guide to speed conversion:
  • Identify conversion factors: One kilometer is equal to 1000 meters, and one hour equals 3600 seconds. Therefore, the conversion factor from km/h to m/s is 0.27778.
  • Apply the conversion: By multiplying the speed in km/h by 0.27778, you convert it to m/s. In this case, multiplying 100 km/h by 0.27778 gives a speed of 27.778 m/s.
Understanding speed conversion ensures accuracy in calculations, especially when different units are used in a problem.
Calculating Distance and Time
In physics, calculating distance and time through the use of formulas is crucial for solving motion-related problems. When analyzing the truck crossing the bridge, we need to calculate both the time it spends on the bridge and the total time until it is entirely off.
To perform these calculations:
  • Utilize the formula for time: The basic formula used is \( \text{time} = \frac{\text{distance}}{\text{speed}} \). It allows us to find out how long it takes for an object to cover a certain distance.
  • Apply this to the problem: For the truck, we calculate the time to cross a 400-meter bridge at a speed of 27.778 m/s, which results in a time of 14.4 seconds.
  • Consider additional times: The problem specifies an additional 0.600 seconds for the truck to fully clear the bridge after reaching its end. Adding this to the crossing time gives the total time of 15.000 seconds.
These calculations show how distance, speed, and time interact, helping solve real-world physics problems effectively.

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Most popular questions from this chapter

A certain car is capable of accelerating at a rate of \(0.60 \mathrm{~m} / \mathrm{s}^{2}\) How long does it take for this car to go from a speed of \(55 \mathrm{mi} / \mathrm{h}\) to a speed of \(60 \mathrm{mi} / \mathrm{h}\) ?

The current indoor world record time in the \(200-\mathrm{m}\) race is \(19.92 \mathrm{~s}\), held by Frank Fredericks of Namibia (1996), while the indoor record time in the one-mile race is \(228.5 \mathrm{~s}\), held by Hicham El Guerrouj of Morroco (1997). Find the mean speed in meters per second corresponding to these record times for (a) the \(200-\mathrm{m}\) event and (b) the one-mile event.

An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at \(+40 \mathrm{ft} / \mathrm{s}^{2}\). After some time \(t_{1}\), the rocket engine is shut down and the sled moves with constant velocity \(v\) for a time \(t_{2}\). If the total distance traveled by the sled is \(17500 \mathrm{ft}\) and the total time is \(90 \mathrm{~s}\), find (a) the times \(t_{1}\) and \(t_{2}\) and (b) the velocity \(v\). At the \(17500-\mathrm{ft}\) mark, the sled begins to accelerate at \(-20 \mathrm{ft} / \mathrm{s}^{2}\). (c) What is the final position of the sled when it comes to rest? (d) How long does it take to come to rest?

A person sees a lightning bolt pass close to an airplane that is flying in the distance. The person hears thunder \(5.0 \mathrm{~s}\) after seeing the bolt and sees the airplane overhead \(10 \mathrm{~s}\) after hearing the thunder. The speed of sound in air is \(1100 \mathrm{ft} / \mathrm{s}\). (a) Find the distance of the airplane from the person at the instant of the bolt. (Neglect the time it takes the light to travel from the bolt to the eye.) (b) Assuming the plane travels with a constant speed toward the person, find the velocity of the airplane. (c) Look up the speed of light in air and defend the approximation used in part (a).

Two students are on a balcony a distance \(h\) above the street. One student throws a ball vertically downward at a speed \(v_{0}\); at the same time, the other student throws a ball vertically upward at the same speed. Answer the following symbolically in terms of \(v_{0}, g\), \(h\), and \(t\). (a) Write the kinematic equation for the \(y\)-coordinate of each ball. (b) Set the equations found in part (a) equal to height 0 and solve each for \(t\) symbolically using the quadratic formula. What is the difference in the two balls' time in the air? (c) Use the time-independent kinematics equation to find the velocity of each ball as it strikes the ground. (d) How far apart are the balls at a time \(t\) after they are released and before they strike the ground?
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