Concept explainers
Frequently, a weapon must be fired at a target that is closer than the weapon’s maximum range. To hit such a target, a weapon has two possible launch angles (Fig. P4.68A): one higher than 45° (θH) and one lower than 45° (θL). Although the displacement of the projectile is the same for the two angles, a projectile launched at θH has a longer flight time and a higher peak position than one launched at θL. 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 θL 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 θL and the high angle θH 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?
Trending nowThis is a popular solution!
Chapter 4 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- Olympus Mons on Mars is the largest volcano in the solar system, at a height of 25 km and with a radius of 312 km. If you are standing on the summit, with what Initial velocity would you have to fire a projectile from a cannon horizontally to clear the volcano and land on the surface of Mars? Note that Mars has an acceleration of gravity of 3.7m/s2 .arrow_forwardIn an article on the use of the sling as a weapon, the author states that a skilled slinger can sling a rock a distance of about 384 m. What is the minimum speed the rock must have when it leaves the sling to travel exactly 384 m? To solve this problem it will be necessary to first determine the required launch angle of the projectile. What launch angle must the projectile have in order to find the minimum speed required to achieve a given horizontal distance?arrow_forwardA fireworks show is choreographed to have two shells cross paths at a height of 154 feet and explode at an apex of 191 feet under normal weather conditions. If the shells have a launch angle θ = 56° above the horizontal, determine the common launch speed v0 for the shells, the separation distance d between the launch points A and B, and the time t from the launch at which the shells explode.arrow_forward
- A rugby player runs with the ball directly toward his opponent’s goal, along the positive direction of an x axis. He can legally pass the ball to a teammate as long as the ball’s velocity relative to the field does not have a positive x component. Suppose the player runs at speed 4.0 m/s relative to the field while he passes the ball with velocity relative to himself. If has magnitude 6.0 m/s, what is the smallest angle it can have for the pass to be legal?arrow_forward*Draw a simple diagram representation for the solution.In a game war, one team sets base on a cliff 15m high and 60m away from the opponent’s base. At what velocity must the attack be launched so that the lower base will be hit? The initial launch is at 20 degrees below the horizontal?arrow_forwardA projectile is fired at 75 degrees above the horizontal line with an initial velocity v0. At which of the following angles the projectile will land at the same distance as it is landed when fired at 75 degrees? A. 15 degrees B. 25 degrees C. 35 degrees D. 45 degreesarrow_forward
- For a projectile fired at an angle of 48 degrees and having an initial velocity of 65 m/s, what is the horizontal component of the initial velocity?arrow_forwardIn the figure, a ball is launched with a velocity of magnitude 6.00 m/s, at an angle of 44.0° to the horizontal. The launch point is at the base of a ramp of horizontal length d1 = 6.00 m and height d2 = 3.60 m. A plateau is located at the top of the ramp. (a) Does the ball land on the ramp or the plateau? When it lands, what are the (b) magnitude and (c) angle of its displacement from the launch point?arrow_forwardIn the figure, a ball is launched with a velocity of magnitude 7.00 m/s, at an angle of 41.0° to the horizontal. The launch point is at the base of a ramp of horizontal length d1 = 6.00 m and height d2 = 3.60 m. A plateau is located at the top of the ramp. Does the ball land on the ramp or the plateau? When it lands, what are the magnitude and angle of its displacement from the launch point?arrow_forward
- A marble is launched from the edge of a table at a angle of 45 ° up from horizontal and goes through the air until it hits the floor. True or False? For such a marble, |vx| (the magnitude of the x-component of the velocity) is decreasing the entire time the marble is airborne.arrow_forwardA projectile is launched from ground level at an angle θ to the top of a cliff which is 195 m away and 155 m high. If the projectile lands right on the cliff edge 7.6 s after it is fired, find the initial velocity of the projectile.arrow_forwardFrom the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 6.50 m/s and angle of 25.0° below the horizontal. It strikes the ground 4.00 s later. the initial coordinates of (d) How far horizontally from the base of the building does the ball strike the ground? (e) Find the height from which the ball was thrown. (f) How long does it take the ball to reach a point 12.0 m below the level of launching?arrow_forward
- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning