the velocity of a particle moving along the x-axis is given by where t is in seconds and is in meters per second. at , the particle is located at . the particle’s equation of motion is
a particles rotates with a constant angular acceleration in a circular path of radius r from rest. after the position vector of the particle sweeps out an angle , the particle’s acceleration makes an angle of 45 degrees with the particle’s velocity. in radians, the angle is given by
a projectile is launched into the air with a speed at an angle with the horizontal direction at . what are the projectile’s normal acceleration at and the radius of curvature of its trajectory at the highest point?
an airplane is flying at a speed of 200 km/h relative to the air, and ground radars show that its speed is 192 km/h. if the wind is blowing from the west to the east, at 56 km/h, the plane must be moving
a all ball is sliding down a frictionless surface, as shown in the figure,
a ball of mass m=0.5kg falls from rest and is subjected to a frictional drag force , where . the ball's maximum velocity is closest to
a ball of mass 1.0 kg is suspended by two wires from a horizontal arm, which is attached to a vertical shaft, as shown in the figure. the shaft executes uniform rotation about its axis such that the tensions in the two wires are equal. the centripetal acceleration of the ball is closest to
object a of mass m is placed on the top of object b, the mass of which is m. the coefficients of static and kinetic friction between a and b are and , respectively. b is placed on a frictionless tabletop. the system is initially at rest, and then a horizontal force f is exerted on a. in order to make sure that there is no relative movement between a and b, we must have
a roadway is designed for traffic moving at a speed of 20 m/s. a curved section of the roadway is a circular arc of 100 m radius. the roadway is banked so that a vehicle can go around the curve with no lateral friction force. the angle at which the roadway is banked is closest to
two balls of the same size, a and b, have masses 4m and m, respectively. the balls are now placed on a frictionless tabletop. initially, a is at rest, and b is moving towards it with a velocity . after they collide, the speed of b becomes , and it moves in a direction perpendicular to . after collision, the magnitude of a's momentum becomes
a spaceship traveling in space with a constant velocity , now fires its engine and exhaust gases are ejected at a constant speed u relative to the spaceship. when the spaceship's speed becomes , its mass reduces to . the value of is closest to
a uniform thin rod is bent into a semicircle of radius r, as shown in the figure. the rod's center of mass is located at point
a satellite is moving in an elliptic orbit around the earth, with the earth at one of the focal points of the ellipse. which of the following statements about the satellite is correct?
which of the following is an accurate statement?
when is the angular momentum of a system constant?
a ball of mass o.8 kg is thrown against a wall. the ball strike the wall horizontally with a speed of 11 m/s, and it bounces back with the same speed. the ball is in contact with the wall for 0.05s. what is the average force exerted on the wall by the ball?
consider three galaxies, alpha, beta and gamma. an observer in beta sees the other two galaxies each moving away from him in opposite directions at speed 0.7c. at waht speed would an observer in alpha see the galaxy gamma moving?