A 5.81 kg ball is attached to the top of a vertical pole with a 2.03 m length of massless string. The ball is struck, causing it to revolve around the pole at a speed of 4.25 m/s in a horizontal circle with the string remaining taut. Calculate the angle, between 0° and 90°, that the string makes with the pole. Take g = 9.81 m/s2.

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.

Keneila is attempting to ski down a 20 m high friction free hill for the first time. she has a speed 10 m/s at the top. what is her kinetic energy when she is a the bottom, 20 m ? (a)2500 j (b)9800 j (c)12300 j (d)3100j (e)15000j

Explain vector addition, triangle method and parallelogram method