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- A particle initially located at the origin has an acceleration of a=3.00jm/s2 and an initial velocity of vi=5.00im/s. Find (a) the vector position of the particle at any time t, (b) the velocity of the particle at any time t, (c) the coordinates of the particle at t = 2.00 s, and (d) the speed of the particle at t = 2.00 s.Check Your Understanding For vector in a rectangular coordinate system, use Equation 2.29 through Equation 2.32 to show that and .Which of the following is a vector a person’s height, the altitude on Mt. Everest, the velocity of a fly, the age of Earth, the boiling point of water, the cost of a book, Earth’s population, or the acceleration of gravity?
- What form does the trajectory of a particle have if the distance from any point Ato point Bis equal to the magnitude of the displacement from Ato B ?In 1999, Robbie Knievel was the first to jump the Grand Canyon on a motorcycle. At a narrow part of the canyon (69.0 m wide) and traveling 35.8 m/s off the takeoff ramp, he reached the other side. What was his launch angle?A ball is tossed horizontally from the highest point of a 75 m building and lands 150 m from the base of the building. Ignore air resistance, and use a coordinate system whose origin is at the highest point of the building, with positive y upwards and positive x in the direction of the throw. How long is the ball in the air for, in seconds?
- From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 8.60 m/s and angle of 18.0° below the horizontal. It strikes the ground 5.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: y0.) xi = yi = (b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity. vi,x = m/s vi,y = m/s (c) Find the equations for the x- and y- components of the position as functions of time. (Use the following as necessary: y0 and t. Let the variable t be measured in seconds.) x = m y = m (d) How far horizontally from the base of the building does the ball strike the ground? m(e) Find the height from which the ball was thrown. m(f) How long does it take the ball to reach a point 10.0 m…A ball is tossed horizontally from the highest point of a 75 m building and lands 150 m from the base of the building. Ignore air resistance, and use a coordinate system whose origin is at the highest point of the building, with positive y upwards and positive x in the direction of the throw. What must have been the initial horizontal component of the velocity, in meters per second?The trajectory of a projectile launched from ground is given by the equationy = -0.035 x2 + 0.75 x, where x and y are the coordinate of the projectile on arectangular system of axes. Find the initial velocity and the angle at which theprojectile is launched.
- From the window of a building, a ball is tossed from aheight y0 above the ground with an initial velocity of 8.00 m/s and angle of 20.0° below the horizontal. It strikes the ground3.00 s later. (a) If the base of the building is taken to be the originof the coordinates, with upward the positive y - direction,what are the initial coordinates of the ball? (b) With the positivex - direction chosen to be out the window, find the x - andy - components of the initial velocity. (c) Find the equations forthe x - and y - components of the position as functions of time.(d) How far horizontally from the base of the building doesthe ball strike the ground? (e) Find the height from which theball was thrown. (f) How long does it take the ball to reach apoint 10.0 m below the level of launching?An artillery shell is fired with an initial velocity of 300 m/s at55.0° above the horizontal. To clear an avalanche, it explodeson a mountainside 42.0 s after firing. What are the x - andy - coordinates of the shell where it explodes, relative to its firingpoint?A bullet is fired from the ground with an initial velocity of 50 m/s that makes with the horizontal an angle of 30°. The y-component of the velocity (v,) of this object after 1 second is?