A projectile is fired from the ground at an angle above the horizontal. At the highest point, after having traveled a horizontal distance D and a vertical distance H from its launch point, it suddenly explodes into two identical fragments A and B. As measured relative to the projectile just before it exploded, Fragment A is moving upward with speed u while Fragment B is moving downward with speed u. The maximum height reached by Fragment A above the ground is 2H. Determine the following, and express them in terms of D, H, and g only: A. The launching angle 0 of the projectile, B. The speed u, C. The speed of fragment B just before it hits the ground.

A projectile is fired from the ground at an angle above the horizontal. At the highest point, after having traveled a horizontal distance D and a vertical distance H from its launch point, it suddenly explodes into two identical fragments A and B. As measured relative to the projectile just before it exploded, Fragment A is moving upward with speed u while Fragment B is moving downward with speed u. The maximum height reached by Fragment A above the ground is 2H. Determine the following, and express them in terms of D, H, and g only: A. The launching angle 0 of the projectile, B. The speed u, C. The speed of fragment B just before it hits the ground.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

A block of mass m = 3 kg starts to slide from rest along a frictionless inclined surface thatmakes an angle of φφ = 300with respect to the horizontal surface.At the lowest points of the inclined surface, a projectile is fired at a speed of vv0 = 12 m/s thatmakes an angle θθ0 = 450 with respect to the horizontal. Our aim of this problem is to find thetime when the projectile will hit the block.
A plane flies horizontally at an altitude h = 4 km with a horizontal speed of 540 km / h ; it launches , without speed relative to the plane , a bomb . The pilot intends to bombard an immobile target , ahead on the ground . To study the motion of the bomb , we consider the system ( XOy ) of origin 0 representing the position of the plane at the instant of launching of the bomb as shown in the adjacent figure . We neglect air resistance . Given g = 9.8 m / s ? 1 ) Determine the launching speed of the bomb . 2 ) Determine the parametric equations of motion of the bomb . 3 ) At what distance « d » from the target should the pilot launch the bomb ? 4 ) Determine the direction and the magnitude of the velocity vector of the bomb at the point of impact with the target 5 ) Determine the position of the plane at the instant of hitting the target . 6 ) Precise , with justification , the trajectory of the bomb with respect to the pilot .
Assume that, at the initial instant to = 0, a particle is thrown with initial speed vo and with an initial angle θo, with respect to a direction parallel to the Earth's surface. In this way, in order to carry out an analytical study of its motion in a simpler way, consider a coordinate system xoy, with its origin at the particle's launch position, and with its positive x axis oriented in the direction of the horizontal motion of the particle and with its positive y-axis oriented vertically upward. In this sense, illustrate (make the force diagrams) the projectile launch, highlighting its main characteristics, and describe algebraically what is asked: a) Equation of the trajectory. (#) do the illustration) b) [0.20] Range. (#) do the illustration) c) Height. (#)(make the illustration)
Problem 4 Derive expressions for the velocity (7) and acceleration (a) vectors in spherical coordinates. That is, transform and a from the Cartesian system of (x, y, z) to (r, 0, 0).
Your friend is standing at the balcony of a building which is H meter high from the ground while you are standing at the parking lot situated at the ground level. Now you realize that you got the wrong keys of your car so you decided to throw the wrong keys to your friend and ask her to drop the original keys. She dropped the keys and at the same instant you threw the keys straight up with a speed of u. Determine the height at which both sets of keys cross each other. Take H=160 m,u=40 m/s and g=10 m/s^2
Suppose two deuterium nuclei (hydrogen nuclei with an additional neutron) are fired at eachother from a large distance. What is the minimum initial velocity they must have in orderto collide? Compare that value with the speed of light in a vacuum. Let the radius of thedeuterium nuclei be 10-15 m.
Handwritten solutions are strictly prohibited.
Your friend is standing at the balcony of a building which is H meter high from the ground while you are standing at the parking lot situated at the ground level. Now you realize that you got the wrong keys of your car so you decided to throw the wrong keys to your friend and ask her to drop the original keys. She dropped the keys and at the same instant you threw the keys straight up with a speed of u. Determine the height at which both sets of keys cross each other. Take H=160 m,u=40 m/s and g=10m/s^2
Consider a particle whose motion is given by [x(t),y(t),z(t)] = [−1,3,−2] + t2 ⋅ [4,2,−3], 0 ≤ t ≤ 2 What is the particle's position at t = 0 ?What is the particle's position at t = 2 ?What is the particle's velocity at t=0?What is the particle's velocity at t=2?What is the particle's speed at t=0?What is the particle's speed at t=2?
A particle is launched from point A with a horizontal speed u and subsequently passes through a vertical opening of height b = 400 mm as shown. Determine the distance d which will allow the landing zone for the particle to also have a width b. Additionally, determine the range of u which will allow the projectile to pass through the vertical opening for this value of d. Your answer is partially correct. d= Answers: ( 3b 788.5 2.76 A u -d- mm m/s) ≤u≤ ( i -b→ 1.95 m/s)
How would I begin to solve this problem? In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for a rocket's position measured from the center of the Earth is given by y(t) = (RE3/2 + 3*(g/2)1/2 REt)2/3 where RE is the radius of the Earth (6.38 ✕ 106 m) and g is the constant acceleration of an object in free fall near the Earth's surface (9.81 m/s2). (a) Derive expressions for vy(t) and ay(t). (Use the following as necessary: g, RE, and t. Do not substitute numerical values; use variables only.)
A particle is launched, from O(0,0) at a speed of 30m/s at an angle of 30°. The time taken by the projectile to reach a vertical wall found at a distance of 10 m is 2 0.75sec - 0.4sec Option 3 O Option 1 2 1sec = 1.5sec O Option 4 O Option 2 Supposing that the angle of impact is 30° (the angle between ở and r- axis), the tangential acceleration aş is: 5/3, opposite to the direction of motion 5 m/s?, opposite to the direction of motion O Option 3 O Option 1 5 m/s?, along the direction of motion 5/3, along the direction of motion O Option 2 Option 4