Concept explainers
A The spiral is an example of a mathematical form appearing in nature, from the visible construction of seashells, pinecones, and galaxies to the movement behavior of certain animals. The position of a hungry animal that moves outward along a spiral path, searching for food, can be written as
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Physics for Scientists and Engineers: Foundations and Connections
- During the battle of Bunker Hill, Colonel William Prescott ordered the American Army to bombard the British Army camped near Boston. The projectiles had an initial velocity of 45 m/s at 35 above the horizon and an initial position that was 35 m higher than where they hit the ground. How far did the projectiles move horizontally before they hit the ground? Ignore air resistance.arrow_forwardFor each of the following velocity vectors, give the vector component, the scalar component, and the magnitude. a. v=35.0jm/s b. vx = 53.0 m/s c. vz = 3.50 m/s d. v=5.30m/sarrow_forwardA During the battle of Bunker Hill, Colonel William Prescott ordered the American Army to bombard the British Army camped near Boston. The projectiles had an initial velocity of v measured in meters per second at an angle above the horizon and an initial position that was h higher than where they hit the ground. How far did the projectiles move horizontally before they hit the ground? Ignore air resistance.arrow_forward
- Some cats can be trained to jump from one location to another and perform other tricks. Kit the cat is going to jump through a hoop. He begins on a wicker cabinet at a height of 1.750 m above the floor and jumps through the center of a vertical hoop, reaching a peak height 3.125 m above the floor. a. With what initial velocity did Kit leave the cabinet if the hoop is at a horizontal distance of 1.544 m from the cabinet? b. If Kit lands on a bed at a horizontal distance of 3.587 m from the cabinet, how high above the ground is the bed?arrow_forwardA baseball diamond consists of four plates arranged in a square. Each side of the square is 90 ft (27.43 m) long. Use an x y coordinate system with the origin at the center of the diamond as shown in Figure P3.18. a. What is the position of each plate in this system? b. What is the distance from home plate to second base?arrow_forwardDock diving is a great form of athletic competition for dogs of all shapes and sizes (Fig. P4.33). Sheba, the American Pit Bull Terrier, runs and jumps off the dock with an initial speed of 9.02 m/s at an angle of 25 with respect to the surface of the water. a. If Sheba begins at a height of 0.84 m above the surface of the water, through what horizontal distance does she travel before hitting the surface of the water? b. Write an expression for the velocity of Sheba, in component form, the instant before she hits the water. c. Determine the peak height above the water reached by Sheba during her jump. FIGURE P4.33arrow_forward
- An arrow is fired with initial velocity v0 at an angle from the top of battlements, a height h above the ground. a. In terms of h, v0, , and g, what is the time at which the arrow reaches its maximum height? b. In terms of h, v0, , and g, what is the maximum height above the ground reached by the arrow?arrow_forwardFrequently, a weapon must be fired at a target that is closer than the weapons maximum range. To hit such a target, a weapon has two possible launch angles (Fig. P4.68A): one higher than 45 (H) and one lower than 45 (L). Although the displacement of the projectile is the same for the two angles, a projectile launched at H has a longer flight time and a higher peak position than one launched at L. Usually, some tactical situation makes one angle preferable to the other. For example, if the projectile must go over some nearby object such as a grove of trees, the higher angle may be desirable. A shorter flight time and therefore L are preferable if the target is mobile. In practice, many weapons are designed to operate either at angles lower than 45 or at angles higher than 45, but not both. Tanks, for example, often must face mobile targets; to minimize the time the target has to move, tanks fire at low angles. Grenades, on the other hand, are launched at high angles because a soldier launching a grenade is often close to the target, but has no armor plating for protection. The high launch angle allows the soldier to stay out of sight by hiding behind some obstacle, and the longer flight time may make it possible for the soldier to move farther from the exploding grenade. FIGURE P4.68 Imagine an unusual scenario in which a large gun mounted on a vehicle is required to hit an explosives factory (Fig. P4.68B). A huge explosion is expected, and there must be time for the gunner to retreat. A grove of trees provides cover. The maximum range of the gun is 17.6 km, and the maximum speed of the vehicle is 80.0 km/h. a. What is the muzzle speed v0? (Muzzle speed is the speed at which the projectile leaves the barrel of the gun.) b. The target is 5.5 km away. Find the low angle L and the high angle H at which the gunner may aim so as to hit the target. c. Find the time the projectile takes to hit the target for both angles. d. Assume the vehicle retreats at its maximum speed (80.0 km/h) to be as far from the ensuing explosion as possible. How far is it from the factory at the time of the explosion for each launch angle?arrow_forwardAnthony carelessly rolls his toy car off a 74.0-cm-high table. The car strikes the floor a horizontal distance of 97.0 cm from the edge of the table. a. What was the velocity with which the car left the table? b. What was the angle of the cars velocity with respect to the floor just prior to impact?arrow_forward
- If a particles speed is always increasing, what are the possible angles between the particles velocity and acceleration?arrow_forwardA physics student stands on a second-story balcony and uses a potato gun to launch a potato horizontally with speed v. The potato has flight time t and lands on the ground a horizontal distance d from the balcony. a. If the launch speed of the potato were doubled, would the time of flight increase, decrease, or stay the same? If the flight time changes, would it double or be halved? Explain. b. If the launch speed of the potato were doubled, would the horizontal distance increase, decrease, or stay the same? If the horizontal distance changes, would it double or be halved? Explain.arrow_forwardIn three different driving tests, a car moves with constant speed v0. In case 1, the car passes over a mark painted on a horizontal, straight section of road. In case 2, the car passes over a mark painted at the crest of a small hill. In case 3, the car passes over a mark painted at the bottom of a small dip. The hill and the dip are circular in profile, with the same radius (Fig. P4.36). Rank the cases from greatest to least according to the magnitude of the acceleration of the car when it passes the mark. Explain. FIGURE P4.36arrow_forward
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