Vector has x, y, and z components of 4.00, 6.00, and 3.00 units, respectively. Calculate (a) the magnitude of role="math" localid="1663647737200" and (b) the angle that makes with each coordinate axis.
(a) The magnitude of is
(b) The vector's angle with the x-axis is , The vector's angle with the y-axis is , The vector's angle with the z-axis is
Let us consider,
In order to determine the magnitude, , this is the formula we utilise.,
Hence, the magnitude of is
The vector's angle with the x-axis
The vector's angle with the y-axis
The vector's angle with the z-axis
Hence, the vector's angle with the x-axis is , The vector's angle with the y-axis is , The vector's angle with the z-axis is
A placekicker must kick a football from a point 36.0 m (about 40 yards) from the goal. Half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 20.0 m/s at an angle of 53.0° to the horizontal.
(a) By how much does the ball clear or fall short of clearing the crossbar?
(b) Does the ball approach the crossbar while still rising or while falling?
Whenever two Apollo astronauts were on the surface of the Moon, a third astronaut orbited the Moon. Assume the orbit to be circular and above the surface of the Moon, where the acceleration due to gravity is role="math" localid="1663698425984" . The radius of the Moon is . Determine (a) the astronaut’s orbital speed and (b) the period of the orbit.
An enemy ship is on the east side of a mountain island as shown in Figure. The enemy ship has maneuvered to within of the -high mountain peak and can shoot projectiles with an initial speed of. If the western shoreline is horizontally from the peak, what are the distances from the western shore at which a ship can be safe from the bombardment of the enemy ship?
Question: 47. (a) A luggage carousel at an airport has the form of a section of a large cone, steadily rotating about its vertical axis. Its metallic surface slopes downward toward the outside, making an angle of 20.0o with the horizontal. A piece of luggage having mass 30.0 kg is placed on the carousel at a position 7.46 m measured horizontally from the axis of rotation. The travel bag goes around once in 38.0 s. Calculate the force of static friction exerted by the carousel on the bag. (b) The drive motor is shifted to turn the carousel at a higher constant rate of rotation, and the piece of luggage is bumped to another position, 7.94 m from the axis of rotation. Now going around once in every 34.0 s, the bag is on the verge of slipping down the sloped surface. Calculate the coefficient of static friction between the bag and the carousel.
63 A model airplane of mass 0.750kg flies with a speed of 35.0 m/s in a horizontal circle at the end of a 60.0m long control wire as shown in above figure a: The forces exerted on the airplane are shown in above figure b: the tension in the control wire, the gravitational force, and aerodynamic lift that acts at inward from the vertical. Compute the tension in the wire, assuming it makes a constant angle of with the horizontal.
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