A train travels between stations 1 and 2, as shown in Figure 2-25. The engineer of the train is instructed to start from rest at station 1 and accelerate uniformly between points A and B, then coast with a uniform velocity between points B and C, and finally accelerate uniformly between points C and D until the train stops at station 2. The distances AB, BC, and CD are all equal, and it takes 3.00 min to travel between the two stations. Assume that the uniform accelerations have the same magnitude, even when they are opposite in direction.

Figure 2.25.

(a) How much of this 3.00 min period does the train spend between points A and B?

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1 min
(b) How much of this 3.00 min period does the train spend between points B and C?

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2 min
(c) How much of this 3.00 min period does the train spend between points C and D?

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3 min

A person walks the path shown in Figure 3-27. The total trip consists of four straight-line paths. At the end of the walk, what is the person's resultant displacement measured from the starting point? Let L = 310.0 m, and let = 40.0°

Figure 3.27.

magnitude

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1 m
direction in degrees

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2° (south of west)

A ship maneuvers to within 2500 m of an island's 1800 m high mountain peak and fires a projectile at an enemy ship 610 m on the other side of the peak, as illustrated in Figure 3-29. If the ship shoots the projectile with an initial velocity of 290 m/s at an angle of 70°, how close to the enemy ship does the projectile land? How close (vertically) does the projectile come to the peak?

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1 m

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2 m

Figure 3.29.

The eye of a hurricane passes over Grand Bahama Island. It is moving in a direction 60.0° north of west with a speed of v₁ = 42.0 km/h. Exactly three hours later, the course of the hurricane shifts due north, and its speed slows to v₂ = 25.0 km/h, as shown in Figure 3-30. How far from Grand Bahama, in kilometers, is the hurricane 4.50 h after it passes over the island?

Figure 3.30.

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1 km

The coefficient of static friction between the 28 kg crate and the 35.0° incline of Figure 4-34 is 0.1. What is the minimum force, F, that must be applied to the crate perpendicular to the incline to prevent the crate from sliding down the incline?

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1 N

Figure 4.34.