Exactly 3.0 s after a projectile is fired into the air from the ground, it is observed to have a velocity v = (8.6i + 4.8j) m/s, where the x axis is horizontal and the y axis is positive upward. Determine {a) the horizontal range of the projectile, (b) its maximum height above the ground, and (c) its speed and angle of motion just before it strikes the ground.
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Exactly 3.0 s after a projectile is fired into the air from the ground, it is observed to have a velocity v = (8.6i + 4.8j) m/s, where the x axis is horizontal and the y axis is positive upward. Determine {a) the horizontal range of the projectile, (b) its maximum height above the ground, and (c) its speed and angle of motion just before it strikes the ground.
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- You can use any coordinate system you like in order to solve a projectile motion problem. To demonstrate the truth of this statement, consider a ball thrown off the top of a building with a velocity v at an angle 0 with respect to the horizontal. Let the building be 54.0 m tall, the initial horizontal velocity be 9.10 m/s, and the initial vertical velocity be 10.5 m/s. Choose your coordinates such that the positive y-axis is upward, and the x-axis is to the right, and the origin is at the point where the ball is released. (a) With these choices, find the ball's maximum height above the ground and the time it takes to reach the maximum height. maximum height above ground time to reach maximum height (b) Repeat your calculations choosing the origin at the base of the building. maximum height above ground time to reach maximum heightFrom the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 9.00 m/s and angle of 21.0° below the horizontal. It strikes the ground 4.00 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. Assume SI units. Do not substitute numerical values; use variables only.) 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. Assume SI units.) 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…A ferryboat is traveling in a direction 22.0° north of east with a speed of 3.16 m/s relative to the water. A passenger is walking with a velocity of 2.53 m/s due east relative to the boat. What is (a) the magnitude and (b) the direction of the velocity of the passenger with respect to the water? Give the directional angle relative to due east. (a) Number (b) Number i Units Units <
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- The position r of a particle moving in an xy plane is given by ř seconds. In unit-vector notation, calculate (a) 7, (b) V , and (c) a for t = 3.00 s. (d) What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t = 3.00 s? Give your answer in the range of (-180°; 180°). (4.00r3 – 1.00t)î + (5.00 – 1.00r4)j with 7 in meters and t in (a) Number i i Units (b) Number ît i Units i (c) Number i i Units (d) Number i UnitsA projectile is fired at an angle above the horizontal. The initial x and y components of its velocity are v=74.9m S and vy=84.9¹ S respectively. At what angle was the projectile fired above the horizontal (in deg)?