A projectile is fired from 3 meters height above level ground with an initial velocity equals to 20 m/s and at an angle equals to 30 degrees above the horizontal level. Note that the air resistance is neglected. the position of a particle with respect to time is defined by: r(t) = rcos(cot )i +rsin(cot)j , where w and r are constants. Demonstrate that the magnitude of the acceleration of the particle is constant.

A projectile is fired from 3 meters height above level ground with an initial velocity equals to 20 m/s and at an angle equals to 30 degrees above the horizontal level. Note that the air resistance is neglected. the position of a particle with respect to time is defined by: r(t) = rcos(cot )i +rsin(cot)j , where w and r are constants. Demonstrate that the magnitude of the acceleration of the particle is constant.

Name: A projectile is fired from 3 meters height above level ground with an
Uploaded: 2024-03-20T06:57:47.000Z
Channel: Bartleby
Description: A projectile is fired from 3 meters height above level ground with an initial velocityequals to 20 m/s and at an angle equals to 30 degrees above the horizontal level. Notethat the air resistance is neglected.the position of a particle with respect t

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter3: Motion In Two Dimensions

Section: Chapter Questions

Problem 6P: At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of...

See similar textbooks

Similar questions

A projectile is fired from 3 meters height above level ground with an initial velocityequals to 20 m/s and at an angle equals to 30 degrees above the horizontal level. Notethat the air resistance is neglected. the position of a particle with respect to time is defined by:r(t) = rcos(cot )i +rsin(cot)j ,where 7 and c are constants.Demonstrate that the magnitude of the acceleration of the particle is constant.
A projectile is fired from point A at angle of 90degrees with respect to the inclined plane. The slope of the plane is 5V:12H. The projectile lands at Point B 70 meters measured along the inclined plane. Determine the Horizontal distance traveled by the projectile. Determine the time traveled to hit B sec and the maximum height reached by the projectile measured from B. What is the initial velocity of the projectile in m/s?
You fire a ball with an initial speed of vo at an angle ø above the surface of an incline, which is itself inclined at an angle 0 above the horizontal. a) Find the distance, measured along the incline, from the launch point to the point when the ball strikes the incline. b) What angle ø gives the maximum range, measured along the incline? Ignore air resistance.
A particle moving in the x-y plane has a position 3, vector given byr = ²i + t³j, where r is in inches and t is in seconds. Calculate the radius of curva- ture p of the path for the position of the particle when t = 2 sec. Sketch the velocity v and the cur- vature of the path for this particular instant.
Imagine an archer preparing to fire an arrow. The archer aims the arrow directly ahead, that is to say, parallel with the ground. Bows are drawn to the corner of the mouth when fired. Let's say, for this particular archer, that puts the arrow 1.8 m (about 5.5 feet) above the ground. Assume that we have measured the initial speed of arrows fired by this archer with this bow and it is 100 m/s. (Ignore wind resistance) a) At what point during the arrow's flight will it be moving the fastest? (Be careful here, think about it. You don't need to do any calculations to figure this out.) b) How long will it take for the arrow to hit the ground?c) How far will the arrow travel during this time period?
A cannon ball is fired with an initial speed of 123 m/s at angle of 60 degrees from the horizontal. Express the initial velocity as a linear combination of its unit vector components. Vo - ( mis) 7 + m/s) ? At the maximum height, the speed of the cannon ball is v= m/s and the magnitude of its acceleration is a- m/s?. The time needed to reach maximum height is t- S. The maximum height reached by the cannon ball is H= m.
You fire a ball with an initial speed vo at an angle Ø above the surface of an incline, which is itself inclined at an angle 0 above the horizontal (see figure). (a) Find the distance, measured along the incline, from the launch point to the point when the ball strikes the incline. (b) What angle Ø gives the maximum range, measured along the incline? Ignore air resistance. Launching a ball from an inclined ramp. vo
At time t = 0 a particle at the origin of an xyz-coordinate system has a velocity vector of vo = i+ 5j – k. The acceleration function of the particle is a(t) = 32r²i + j+ (cos 21)k. Find the speed of the particle at time t = 1. Round your answer to two decimal places.
I only need help with part d. A ball is thrown with initial speed v0 up an inclined plane. The plane is inclinedat an angle φ above the horizontal, and the ball is launched at an angle α > φ above thehorizontal. (a) How much time does it take for the ball to land? (b) How far up the hill willthe ball land? (c) For what angle α will the range from part (b) be a maximum? (d) What isthe maximum range?
A projectile is fired at time t = 0.0 s, from point 0 at the edge of a cliff, with initial velocity components of vox x = 30 m/s and Voy = 100 m/s. The projectile rises, then falls into the sea at Point P. The time of flight of projectile is 25.0 seconds. What is the magnitude of the velocity at time = 15 seconds?
A projectile, launched at A with an initial velocity of 105 m/s at the angle theta = 57 degrees, impacts the vertical wall at B. Neglecting air resistance, calculate the height h. Use 3 decimal places
On level ground a shell is fired with an initial velocity of40.0 m/s at 60.0° above the horizontal and feels no appreciable air resistance. How long does it take the shell to reach its highest point?