91Ó°ÊÓ

A uniform rod of length \(30.0 \mathrm{cm}\) is bent into the shape of an inverted U. Each of the three sides is of length \(10.0 \mathrm{cm} .\) Find the location, in \(x\) - and \(y\) -coordinates, of the CM as measured from the origin.

An inexperienced catcher catches a \(130 \mathrm{km} / \mathrm{h}\) fastball of mass \(140 \mathrm{g}\) within \(1 \mathrm{ms}\), whereas an experienced catcher slightly retracts his hand during the catch, extending the stopping time to 10 ms. What are the average forces imparted to the two gloved hands during the catches?

A stationary 0.1-g fly encounters the windshield of a \(1000-\mathrm{kg}\) automobile traveling at \(100 \mathrm{km} / \mathrm{h} .\) (a) What is the change in momentum of the car due to the fly? (b) What is the change of momentum of the fly due to the car? (c) Approximately how many flies does it take to reduce the car's speed by \(1 \mathrm{km} / \mathrm{h} ?\)

A 0.15-kg baseball is pitched with a speed of \(35 \mathrm{m} / \mathrm{s}\) \((78 \mathrm{mph}) .\) When the ball hits the catcher's glove, the glove moves back by \(5.0 \mathrm{cm}(2 \text { in. })\) as it stops the ball. (a) What was the change in momentum of the baseball? (b) What impulse was applied to the baseball? (c) Assuming a constant acceleration of the ball, what was the average force applied by the catcher's glove?

A projectile of mass \(2.0 \mathrm{kg}\) approaches a stationary target body at \(8.0 \mathrm{m} / \mathrm{s} .\) The projectile is deflected through an angle of \(90.0^{\circ}\) and its speed after the collision is $6.0 \mathrm{m} / \mathrm{s}$ What is the speed of the target body after the collision if the collision is perfectly elastic?

A radioactive nucleus is at rest when it spontaneously decays by emitting an electron and neutrino. The momentum of the electron is $8.20 \times 10^{-19} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$ and it is directed at right angles to that of the neutrino. The neutrino's momentum has magnitude $5.00 \times 10^{-19} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$ (a) In what direction does the newly formed (daughter) nucleus recoil? (b) What is its momentum?

A 60.0 -kg woman stands at one end of a \(120-\) kg raft that is $6.0 \mathrm{m}\( long. The other end of the raft is \)0.50 \mathrm{m}$ from a pier. (a) The woman walks toward the pier until she gets to the other end of the raft and stops there. Now what is the distance between the raft and the pier? (b) In (a), how far did the woman walk (relative to the pier)?

A police officer is investigating the scene of an accident where two cars collided at an intersection. One car with a mass of \(1100 \mathrm{kg}\) moving west had collided with a \(1300-\mathrm{kg}\) car moving north. The two cars, stuck together, skid at an angle of \(30^{\circ}\) north of west for a distance of \(17 \mathrm{m} .\) The coefficient of kinetic friction between the tires and the road is \(0.80 .\) The speed limit for each car was $70 \mathrm{km} / \mathrm{h} .$ Was either car speeding?

A jet plane is flying at 130 m/s relative to the ground. There is no wind. The engines take in \(81 \mathrm{kg}\) of air per second. Hot gas (burned fuel and air) is expelled from the engines at high speed. The engines provide a forward force on the plane of magnitude \(6.0 \times 10^{4} \mathrm{N} .\) At what speed relative to the ground is the gas being expelled? [Hint: Look at the momentum change of the air taken in by the engines during a time interval \(\Delta t .\) ] This calculation is approximate since we are ignoring the \(3.0 \mathrm{kg}\) of fuel consumed and expelled with the air each second.