b A marksman aimed his rifle at the bull's eye of a target 50m away. If the bullet's speed is 350 m/s, how far below the bull's eye does the bullet strikes the target in centimeters.
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- Figure P2.33 shows the y-position (in blue) of a particle versus time. a. What is the average velocity of the particle during the time interval t = 1.00 s to t = 3.50 s? b. Using the tangent to the curve (shown as the orange line in the figure), what is the instantaneous velocity of the particle at t = 1.50 s? c. At what time is the velocity of the particle equal to zero? FIGURE P2.33Pete and Sue, two reckless teenage drivers, are racing eastward along a straight stretch of highway. Pete is traveling at 98.0 km/h, and Sue is chasing him at 125 km/h. a. What is Petes velocity with respect to Sue? b. What is Sues velocity with respect to Pete? c. If Sue is initially 325 m behind Pete, how long will it take her to catch up to him?Two sprinters start a race along a straight track at the same time and cross the finish line at the same time. a. Are their average velocities necessarily equal? Explain. b. Are their instantaneous velocities necessarily always equal? Explain. c. Are their final velocities necessarily equal? Explain.
- While strolling downtown on a Saturday Afternoon, you stumble across an old car show. As you are walking along an alley toward a main street, you glimpse a particularly stylish Alpha Romeo pass by. Tall buildings on either side of the alley obscure your view, so you see the car only as it passes between the buildings. Thinking back to your physics class, you realize that you can calculate the cars acceleration. You estimate the width of the alleyway between the two buildings to be 4 m. The car was in view for 0.5 s. You also heard the engine rev when the car started from a red light, so you know the Alpha Romeo started from rest 2 s before you first saw it. Find the magnitude of its acceleration.(a) A light-rail commuter train accelerates at a rate of 1.35m/s2 . How long does it take to reach its top speed of 80.0 km/h, starting from rest? (b) The same train ordinarily decelerates at a rate of 1.65m/s2 . How long does it take to came to a stop from its top speed? (c) In emergencies, the train can decelerate more rapidly, coming to rest from 80.0 km/h in 8.30 s. What is its emergency acceleration in meters per second sqquared?In a cartoon program, Peter tosses his baby, Stewie, up into the air to keep the child entertained. Stewie reaches a maximum height of 0.873 m above the release point. Suppose the positive y axis points upward, a. With what initial velocity was Stewie thrown? b. How much time did it take Stewie to reach the peak height?
- A driver uniformly accelerates his car such that a=6.851im/s2. a. Assuming he starts from rest, find the velocity of the car after it has accelerated for 4.55 s. b. If immediately after that 4.55 s the driver lays off the accelerator, slams on the brakes, and comes to a stop in the subsequent 5.62 s, what is the acceleration he experiences during that time, assuming the acceleration is constant?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.Tadeh launches a model rocket straight up from his backyard that takes 4.50 s to reach its maximum altitude. (After launch, the rockets motion is only influenced by gravity.) a. What is the rockets initial velocity? b. What is the maximum altitude reached by the rocket?
- An experimentalist in a laboratory finds that a particle has a helical path. The position of this particle in the laboratory frame is given by r(t)=Rcost+Rsint+vztk where R, vz, and are constants. A moving frame has velocity (vM)L=vzk relative to the laboratory frame. a. What is the path of the particle in the moving frame? b. What is the velocity of the particle as a function of time relative to the moving frame? c. What is the acceleration of the particle in each frame? d. How should the acceleration in each frame be related? Does your answer to part (c) make sense? Explain.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?Frequently, 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?