The energy of bowling ball rolling down the lane is 150J. If it is rolling at 7.5 m/s, find the mass of the bowling ball.

Problem 6: A space vehicle of mass m=300 kg has a speed v=1000 m/s along the positive x-direction. At some instant, it separates into two pieces, with mass m1=100 kg and m2=200 kg. The first piece moves with a speed of 600 m/s at an angle of 300 relative to the x-axis. (a) The speed of the second piece is ________ (b) The kinetic energy of the second piece after the explosion is __________

QIIII: A thin uniform rod of mass Mr and length L is suspended from the ceiling and mounted on a horizontal frictionless axle at the top. The rod is initially at rest in its equilibrium position when a ball of play dough, of mass mb, strikes the rod at its lower end and remains stuck to the rod. The sticky ball is thrown with an initial speed v0 at a 60 degree angle from the horizontal direction, and strikes the rod when it reaches the top of its trajectory, as shown in Fig.4. The acceleration due to gravity has magnitude g and air resistance is negligible.  a. Determine the velocity of the ball of play dough right before it sticks to the rod. Use the x- y coordinate system defined in Fig.4.   b. Determine the angular velocity of the rod+ball system right after the collision. Take counterclockwise as positive.   c. - Establish the differential equation satisfied by the rod+ball system after the collision and determine the angular frequency of the system. You may assume that the small…

A gun fires a 21-gram bullet on a 1.8 kg wooden block hanging vertically at the end of string (The other end of the string is attached to a ceiling). The bullet embeds in the block, which swings upward a height of H. The speed of the bullet when leaving the gun is 250 m/s. Find H.

An archer shoots an arrow toward a 300-g target that is sliding in her direction at a speed of 2.15 m/s on a smooth, slippery surface. The 22.5-g arrow is shot with a speed of 35.5 m/s and passes through the target, which is stopped by the impact. What is the speed of the arrow after passing through the target?

The dome at Monticello is 13.6 m high. If a pebble with a mass of 15g is thrown horizontally from the top of the dome at a velocity of 3.5 m/s, use the Law of Conservation of energy to determine its speed the instant before it hits the ground.