A radar antenna is tracking a satellite orbiting the earth. At a certain time, the radar screen shows the satellite to be 162 km away. The radar antenna is pointing upward at an angle of 62.3° from the ground. Find the x and y components (in km) of the position of the satellite.
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The punter on a football team tries to kick a football so that it stays in the air for a long “hang time.” If the ball is kicked with an initial velocity of 25.0 m/s at an angle of 60.0° above the ground, what is the “hang time”?
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A bullet is fired from a rifle that is held 1.6 m above the ground in a horizontal position. The initial speed of the bullet is 1100 m/s. Find (a) the time it takes for the bullet to strike the ground and (b) the horizontal distance traveled by the bullet.
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Suppose that the plane in Example 2 is traveling with twice the horizontal velocity-that is, with a velocity of +230 m/s. If all other factors remain the same, determine the time required for the package to hit the ground.
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On a spacecraft two engines fire for a time of 565 s. One gives the craft an acceleration in the x direction of ax=5.10 m/s2, while the other produces an acceleration in the y direction of ay=7.30 m/s2. At the end of the firing period, the craft has velocity components of vx=3775 m/s and vy=4816 m/s. Find the magnitude and direction of the initial velocity. Express the direction as an angle with respect to the +x axis.
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As preparation for this problem, review Conceptual Example 9. The drawing shows two planes each dropping an empty fuel tank. At the moment of release each plane has the same speed of 135 m/s, and each tank is at the same height of 2.00 km above the ground. Although the speeds are the same, the velocities are different at the instant of release, because one plane is flying at an angle of 15.0° above the horizontal and the other is flying at an angle of 15.0° below the horizontal. Find the magnitude and direction of the velocity with which the fuel tank hits the ground if it is from (a) plane A and (b) plane B. In each part, give the directional angles with respect to the horizontal.
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The highest barrier that a projectile can clear is 13.5 m, when the projectile is launched at an angle of 15.0° above the horizontal. What is the projectile’s launch speed?
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Before starting this problem consult Interactive Solution 3.67 . A golfer, standing on a fairway, hits a shot to a green that is elevated 5.50 m above the point where she is standing. If the ball leaves her club with a velocity of 46.0 m/s at an angle of 35.0° above the ground, find the time that the ball is in the air before it hits the green.
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A diver springs upward from a board that is three meters above the water. At the instant she contacts the water her speed is 8.90 m/s and her body makes an angle of 75.0° with respect to the horizontal surface of the water. Determine her initial velocity, both magnitude and direction.
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Mario, a hockey player, is skating due south at a speed of 7.0 m/s relative to the ice. A teammate passes the puck to him. The puck has a speed of 11.0 m/s and is moving in a direction of 22° west of south, relative to the ice. What are the magnitude and direction (relative to due south) of the puck’s velocity, as observed by Mario?
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An oceanliner is heading due north with a speed of 8.5 m/s relative to the water. A small sailboat is heading 45° east of north with a speed of 1.0 m/s relative to the water. Find the relative velocity (magnitude and direction) of the sailboat as observed by the passengers on the ocean liner. Determine the directional angle relative to due north.
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An airplane is flying with a velocity of 240 m/s at an angle of 30.0° with the horizontal, as the drawing shows. When the altitude of the plane is 2.4 km, a flare is released from the plane. The flare hits the target on the ground. What is the angle q ?
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A jetliner can fly 6.00 hours on a full load of fuel. Without any wind it flies at a speed of 
m/s. The plane is to make a round-trip by heading due west for a certain distance, turning around, and then heading due east for the return trip. During the entire flight, however, the plane encounters a 57.8-m/s wind from the jet stream, which blows from west to east. What is the maximum distance that the plane can travel due west and just be able to return home?
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Concept Simulation 3.2 reviews the general principles in this problem. A projectile is launched from ground level at an angle of 12.0° above the horizontal. It returns to ground level. To what value should the launch angle be adjusted, without changing the launch speed, so that the range doubles?
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