An airplane with a speed of 82.3 m/s is climbing upward at an angle of 57.4° with respect to the horizontal. When the plane's altitude is 708 m, the pilot releases a package. (a) Calculate the distance along the ground, measured from a point directly beneath the point of release, to where the package hits the earth. (b) Relative to the ground, determine the angle of the velocity vector of the package just before impact. (a) Number i (b) Number i Units Units
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- An airplane with a speed of 93.6 m/s is climbing upward at an angle of 63.6° with respect to the horizontal. When the plane's altitude is 907 m, the pilot releases a package. (a) Calculate the distance along the ground, measured from a point directly beneath the point of release, to where the package hits the earth. (b) Relative to the ground, determine the angle of the velocity vector of the package just before impact. Use negative sign if the angle is below the horizontal.A marble is thrown horizontally with a speed of 12.0 m/s from the top of a building. When it strikes the ground, the marble has a velocity that makes an angle of 65 ° with the horizontal. From what height above the ground was the marble thrown?A ball is launched horizontally from the top of a 100 m tall building and lands 150 m (horizontal distance) from the base of the building. Ignore air resistance. (a) How long in seconds is the ball in the air? (b) What must have been the initial horizontal component of the velocity in m/s? (c) What is the vertical component of the velocity in m/s just before the ball hits the ground? (d) What is the speed or magnitude of the resultant velocity (including both the horizontal and vertical components) in m/s of the ball just before it hits the ground?
- A car is 3.0 km west of a traffic light at t = 0 and 7.0 km east of the light at t = 8.0 min. Assume the origin of the coordinate system is the light and the positive x direction is eastward. (a) what are the car’s position vectors at these two times? (b) what is the car’s displacement between 0 min and 6.0 min?In the figure here, a ball is thrown up onto a roof, landing 4.40 s later at height h = 24.0 m above the release level. The ball's path just before landing is angled at 0= 63.0° with the roof. (a) Find the horizontal distance d it travels. (Hint: One way is to reverse the motion, as if it is on a video.) What are the (b) magnitude and (c) angle (relative to the horizontal) of the ball's initial velocity? 0000 (a) Number i (b) Number i (c) Number i Unit Unit UnitFrom 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. (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 below the level of launching? s
- A ball is tossed from an upper-story window of a building. The ball is given an initial velocity of 8.10 m/s at an angle of 19.0° below the horizontal. It strikes the ground 5.00 s later. (a) How far horizontally from the base of the building does the ball strike the ground? m(b) Find the height from which the ball was thrown. m(c) How long does it take the ball to reach a point 10.0 m below the level of launching? sA plane flies 493 km east from city A to city B in 45.0 min and then 983 km south from city B to city C in 1.30 h. For the total trip, what are the (a) magnitude and (b) direction of the plane's displacement, the (c) magnitude and (d) direction of its average velocity, and (e) its average speed? Give your angles as positive or negative values of magnitude less than 180 degrees, measured from the +x direction (east). (a) Number i Units (b) Number Units (c) Number i Units (d) Number i Units (e) Number Units IIA placekicker is about to kick a field goal. The ball is 21.7 m from the goalpost. The ball is kicked with an initial velocity of 19.1 m/s at an angle above the ground. Between what two angles, 0₁ and 02, will the ball clear the 2.67-m-high crossbar? Give your answers as (a) the smaller angle and (b) the larger angle. (Hint: The following trigonometric identities may be useful: sec 0 = 1/(cos) and sec²0 = 1 + tan²0.) (a) Number (b) Number Units Units 0₂
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