Concept explainers
In the absence of air resistance, a projectile that lands at the elevation from which it was launched achieves maximum range when launched at a 45° angle. Suppose a projectile of mass m is launched with speed v0into a headwind that exerts a constant, horizontal retarding force
a. Find an expression for the angle at which the range is maximum.
b. By what percentage is the maximum range of a 0.50 kg ball reduced if Fwind= 0.60 N?
Trending nowThis is a popular solution!
Chapter 8 Solutions
PHY F/SCIENTIST MOD MASTERING 24 MO
- A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of vi= 18.0 m/s. The cliff is h = 50.0 m above a body of water as shown in Figure P3.19. (a) What are the coordinates of the initial position of the stone? (b) What are the components of the initial velocity of the stone? (c) What is the appropriate analysis model for the vertical motion of the stone? (d) What is the appropriate analysis model for the horizontal motion of the stone? (e) Write symbolic equations for the x and y components of the velocity of the stone as a function of time. (f) Write symbolic equations for the position of the stone as a function of time. (g) How long after being released does the stone strike the water below the cliff? (h) With what speed and angle of impact does the stone land?arrow_forwardA firefighter, a distance d from a burning building, directs a stream of water from a fire hose at angle i above the horizontal as shown in Figure P4.11. If the initial speed of the stream is vi, at what height h does the water strike the building? Figure P4.11arrow_forwardA TI Yo Ac As Inv Eva Knc need to: 1. Ignore air resistance when answering all parts of this question. a. A golf ball is hit at 60.0° to the horizontal with an initial velocity of 1.50 x 102 ms¹. It lands at the same height from which it is hit. i. Show that the initial vertical velocity of the ball is 1.30 x 102ms¯ (1) 1/2 ii. Find the time of flight of the golf ball. iii. Calculate the range of the ball. KA1 (1) KA2 (3) KA2 (2) b. A baseball is hit at the same angle and initial speed as the golf ball in part a. However, its initial height is 1.3m above the ground. Explain why the baseball will travel further than the golf ball from part a.arrow_forward
- A baseball player hits a ball at 100 mph, with an initial height of 3 feet at an angle of elevation of30°, at Boston’s Fenway Park. The ball flies towards the gamed “Green Monster”, a wall 37 feethigh located 310 feet from home plate.a. Show that as hit, the ball hits the wall.b. Show that if the angle of elevation is 21°, the ball clears the Green Monster.arrow_forwardA 2 kg ball was thrown in the air from an angle of 30° moving with a velocity v= 20 m/s. Assume the initial starting point is on the ground. a. Illustrate a diagram of the scenario. b. Compute for the components of velocity. c Compute the half time of flight. d. Compute for the maximum height e. Find the range of the trajectory.arrow_forwardAnswer a,b, & c:arrow_forward
- You fire a ball with an initial speed V0 at an angle (ϕ) above the surface of an incline, which is itself inclined at an angle (θ) above the horizontal (Figure below). a. Find the distance, measured along the incline, from the launch point to the point when the ball strikes the incline. b. What angle ϕ gives the maximum range, measured along the incline? Ignore air resistance. c. Since there's no air resistance, this is a problem in projectile motion. The goal is to find the point where the ball's parabolic trajectory intersects the incline. It is best to choose the x-axis to be horizontal and direct to the right, the y-axis to be vertical and direct to the up, and the origin to be at the point where the ball is fired. In the projectile equations, the launch angle α0 is measured from the horizontal. What is this angle in terms of (θ) and (ϕ)?arrow_forwardA rock is thrown off a cliff at an angle of51ºwith respect to the horizontal. The cliff is 110 m high. The initial speed of the rock is 30 m/s. a.How high above the edge of the cliff does the rock rise? b.How far has it moved horizontally when it is at maximum altitude? ( c.How long after the release does it hit the ground? d.What is the range of the rock? e.What are the horizontal and vertical positions of the rock relative to the edge of the cliff att= 2.0 s,t= 4.0 s, andt= 6.0 s?arrow_forwardKara is setting up a tee-shirt cannon for a community event. The angle of the cannon can be adjusted, but all projectiles leave the cannon at 25 meters per second. If Kara sets the angle of the cannon to be 20.o above horizontal, what will be the range of the projectiles? 64 m 61 m 41 m 25 marrow_forward
- A projectile is launched with an initial velocity of v0 and an elevation angle of zero degrees. If the projectile were launched with the same initial velocity from the surface of Earth (g=9.80 m/s2) as from the surface of Mars (g=3.72 m/s2), which of the following would be true? a. Both the time of flight and the range would be larger on Mars. b. Both the time of flight and the range would be larger on Earth. c. The time of flight is greater on Earth but the range would be greater on Mars. d. The time of flight is greater on Mars but the range would be greater on Earth. e. The time of flight and the range would be the same on both planets.arrow_forwardnt. 8. A cannonball is shot from a cannon at 45-degree angle: a. In Galeleo's Kinetic equations, which variable must be constant for the equations to give the correct results? b. If the x axis represents the horizonal axis, what is the value of ax? C. Assuming there was no air resistance, would final velocity of the cannonball be (1) greater than initial velocity, (2) less than initial velocity, or (3) the same as initial velocity when is at its maximum height? d. Assuming there was air resistance, would final velocity of the cannonball be (1) greater than initial velocity, (2) less than initial velocity, or (3) the same as initial velocity when is at its maximum height?arrow_forwardI need help with thisarrow_forward
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill