Two identical 1350-kg automobiles A and B are at rest with their brakes released when B is struck by a 5400-kg truck C that is moving to the left at 8 km/h. A second collision then occurs when B strikes A. Assuming the first collision is perfectly plastic and the second collision is perfectly elastic, determine the velocities of the three vehicles just after the second collision.

Cars B and C are at rest with their brakes off. Car A plows into B at high speed, pushing B into C. If the collisions are completely inelastic, what fraction of the initial energy is dissipated in car C? Initially the cars are identical.

A crash test is performed between a $4500 \mathrm{~lb}$ SUV $A$ and a compact car $B$. A transducer measures the force during the impact, and the force $\mathbf{P}$ varies as shown. Knowing that the SUV is traveling $30 \mathrm{~mph}$ when it hits the car, determine the speed of the SUV immediately after the impact.

Three identical cars are being unloaded from an automobile carrier. Cars B and C have just been unloaded and are at rest with their brakes off when car A leaves the unloading ramp with a velocity of 5.76 ft/s and hits car B, which hits car C. Car A then again hits car B. Knowing that the velocity of car B is 5.04 ft/s after the first collision, 0.630 ft/s after the second collision, and 0.709 ft/s after the third collision, determine (a) the final velocities of cars A and C, (b) the coefficient of restitution for each of the collisions

A 30-g bullet is fired with a horizontal velocity of 450 m/s and becomes embedded in block B, which has a mass of 3 kg. After the impact, block B slides on 30-kg carrier C until it impacts the end of the carrier. Knowing the impact between B and C is perfectly plastic and the coefficient of kinetic friction between B and C is 0.2, determine (a) the velocity of the bullet and B after the first impact, (b) the final velocity of the carrier.

Plot the polynomial $y = 0.1 x ^ { 5 } - 0.2 x ^ { 4 } - x ^ { 3 } + 5 x ^ { 2 } - 41.5 x + 235$ in the domain $- 6 \leq x \leq 6 .$ First create a vector for $x ,$ next use the polyval function to cal- culate $y ,$ and then use the plot function.

The velocities of two steel blocks before impact are as shown. Knowing that the velocity of block $B$ after the impact is observed to be $2.5 \mathrm{~m} / \mathrm{s}$ to the right, determine the coefficient of restitution between the two blocks.

How would you say 'They plan to brush their hair with the brush ' in Spanish?

You bail out of a helicopter and immediately open your parachute, so your downward velocity satisfies the initial value problem

$$\frac { d v } { d t } = 32 - 1.6 v , \quad v ( 0 ) = 0$$

(with $t$ in seconds and $v$ in ft/s). Use the improved Euler method with a programmable calculator or computer to approximate the solution for $0 \leqq t \leqq 2$, first with step size h D 0:01 and then with $h = 0.005$, rounding off approximate v-values to three decimal places. What percentage of the limiting velocity $20$ ft/s has been attained after $1$ second? After $2$ seconds?

A mining company is considering a new project. Because the mine has received a permit, the project would be legal; but it would cause significant harm to a nearby river. The firm could spend an additional $10 million at Year 0 to mitigate the environmental problem, but it would not be required to do so. Developing the mine (without mitigation) would cost$60 million, and the expected cash inflows would be $20 million per year for 5 years. If the firm does invest in mitigation, the annual inflows would be$21 million. The risk-adjusted WACC is 12%. a. Calculate the NPV and IRR with and without mitigation. b. How should the environmental effects be dealt with when this project is evaluated? c. Should this project be undertaken? If so, should the firm do the mitigation?

You are meeting a friend at Fort Myers Airport. According to the Bureau of Transportation Statistics, in 2009 flights into Fort Myers were on time 81.3% of the time, but Southwest had a better record and is on time 84.5% of the time. You cannot remember what airline she is taking but you know that in the past she has flown on Southwest 70% of the time. The plane is late. What is the probability she is on Southwest?

Solve the given initial value problem (differential equation subject to a specified condition. $\frac{d x}{d t}=\frac{\sin (\sqrt{t})}{\sqrt{t}};$ x(0) = -1

Find $\alpha$ and $Z_{0}$ of a distortionless line whose $R^{\prime}=2 \Omega / \mathrm{m}$ and $G^{\prime}=2 \times 10^{-4} \mathrm{S} / \mathrm{m}$.

Rutherford's experiment consisted of beaming positively charged particles at thin gold foil. According to Rutherford, where in an atom are these particles located?