Explosive bolts separate a 950 kg communications satellite from its 640 kg booster rocket, imparting a $350-\mathrm{N} \cdot \mathrm{s}$ impulse. At what relative speed do satellite and booster separate?

Why are cars designed so that their front ends crumple during an accident?

While standing on frictionless ice, you (mass 65.0 kg ) toss a 4.50 kg rock with initial speed 12.0 m/s. If the rock is 15.2 m from you when it lands,

(a) at what angle did you toss it?

(b) How fast are you moving?

Verify explicitly that kinetic energy is conserved in the collision of the earlier exercise.

Mass m, moving at speed 2 v, approaches mass 4 m, moving at speed v. The two collide elastically head-on. Find expressions for their subsequent speeds.

You're a production engineer in a cookie factory, where mounds of dough drop vertically onto a conveyor belt at the rate of one 12-g mound every $2 \mathrm{~s}$. You're asked to design a mechanism that will keep the conveyor belt moving at a constant $50 \mathrm{~cm} / \mathrm{s}$. What average force must the mechanism exert on the belt?

A 62 kg sprinter stands on the left end of a 190 kg cart moving leftward at 7.1 m/s. She runs to the right end and continues horizontally off the cart. What should be her speed relative to the cart so that once she's off the cart, she has no horizontal velocity relative to the ground?

Assuming equal-mass pieces in earlier exercise, find the angles of the two velocities relative to the direction of motion before the explosion.

A 60 kg astronaut floating in space simultaneously tosses away a 14-kg oxygen tank and a 5.8-kg camera. The tank moves in the x-direction at 1.6 m/s, and the astronaut recoils at $0.85 \mathrm{~m} / \mathrm{s}$ in a direction $200^{\circ}$ counterclockwise from the $x$-axis. Find the camera's velocity.

A 42-g firecracker is at rest at the origin when it explodes into three pieces. The first, with mass 12 g, moves along the x-axis at 35 m/s. The second, with mass 21 g, moves along the $y$-axis at 29 $\mathrm{m} / \mathrm{s}$. Find the velocity of the third piece.

A cylindrical concrete silo is $4.0 \mathrm{~m}$ in diameter and $30 \mathrm{~m}$ high. It consists of a $6000 \mathrm{~kg}$ concrete base and $38,000 \mathrm{~kg}$ cylindrical concrete walls. Locate the center of mass of the silo $(a)$ when it's empty and $(b)$ when it's two-thirds full of silage whose density is $800 \mathrm{~kg} / \mathrm{m}^3$. Neglect the thickness of the walls and base.

A Urenium-238 nucleus is moving in the x-direction at 500000 m/s when it decays into an alpha particle $\left({ }^4 \mathrm{He}\right)$ and a ${ }^{234} \mathrm{Th}$ nucleus. The alpha moves at $1.4 \times 10^7 \mathrm{~m} / \mathrm{s}$ at $22^{\circ}$ above the $x$-axis. Find the recoil velocity of the thorium.

An hourglass is inverted and placed on a scale. Compare the scale readings $(a)$ before sand begins to hit the bottom; $(b)$ while sand is hitting the bottom; and $(c)$ when all the sand is on the bottom.

Masses m and 3m approach at the same speed v and undergo a head-on elastic collision. Show that mass 3m stops, while mass m rebounds at speed 2 v.