Apopular ride at some playgrounds consists of two circular disks joined by rungs . the center of the unit is attached to a horizontal axle around which the unit rotates. the rotational inertia of the unit is 550 kg⋅m2 , and its radius is 1.00 m. a 30-kg child runs and grabs the bottom rung of the ride when it is initially at rest. because the child can pull herself up to meet the rung at waist height, treat her as a particle located on the rung. the friction between unit and axle is minimal and can be ignored. what is the minimum speed v the child must have when she grabs the bottom rung in order to make the unit rotate about its axle and carry her over the top of the unit? express your answer with the appropriate units.

Scientists use laser range-finding to measure the distance to the moon with great accuracy. a brief laser pulse is fired at the moon, then the time interval is measured until the "echo" is seen by a telescope. a laser beam spreads out as it travels because it diffracts through a circular exit as it leaves the laser. in order for the reflected light to be bright enough to detect, the laser spot on the moon must be no more than 1.0 km in diameter. staying within this diameter is accomplished by using a special large-diameter laser. part a if λ = 540nm , what is the minimum diameter of the circular opening from which the laser beam emerges? the earth-moon distance is 384,000 km. express your answer to two significant figures and include the appropriate units.

The friction of the water on a boat produces an acceleration of -10. m/s2. if the boat is traveling at 30. m/s and the motor is shut off, how long it take the boat to slow down to 5.0 m/s?

1. explain how you calculate the net force in any direction on the box. 2. suppose an upward force of 15n is added to the box. what will be the net vertical force on the box? 3. what force could be applied to the box to make the net force in the horizontal direction zero? explain. 4. suppose a force of 25n to the right is added to the box. what will be the net force to the right?