In a downhill ski race, surprisingly, little advantage is gained by getting a running start. (This is because the initial kinetic energy is small compared with the gain in gravitational potential energy on even small hills.) To demonstrate this, find the final speed and the time taken for a skier who skies 70.0 m along a $30^{\circ}$ slope neglecting friction: (a) Starting from rest. (b) Starting with an initial speed of 2.50 m/s. (c) Does the answer surprise you? Discuss why it is still advantageous to get a running start in very competitive events.

How much speed does a freely falling object gain during each second of fall?

A 100-g toy car is propelled by a compressed spring that starts it moving. The car follows the curved track. Show that the final speed of the toy car is 0.687 m/s if its initial speed is 2.00 m/s and it coasts up the frictionless slope, gaining 0.180 m in altitude.

If an atom has the electron configuration

$$1s^22s^22p^3$$

how many electrons must it gain to achieve an octet?

(a) Calculate the force needed to bring a 950-kg car to rest from a speed of 90.0 km/h in a distance of 120 m (a fairly typical distance for a non-panic stop). (b) Suppose instead the car hits a concrete abutment at full speed and is brought to a stop in 2.00 m. Calculate the force exerted on the car and compare it with the force found in part (a).

Use the substitution v=y' to change the harmonic oscillator into a planar system having form

$$\begin{array}{l} y^{\prime}=v, \\ v^{\prime}=f(y, v). \end{array}$$

Use Euler's method to provide an approximate solution over the given time interval using the given step sizes. Provide a plot of v versus y for each step size. y''+9y=0, y(0)=0, y'(0)=-4, [0, $2 \pi$], h=0.1, 0.01, 0.001

Use mathematical induction to show that the summation formula holds for all natural numbers. $1^{3}+2^{3}+3^{3}+\cdots+n^{3}=\frac{n^{2}(n+1)^{2}}{4}$

Find each product. $4(-10)(-3)$

A toy gun uses a spring with a force constant of 300 N/m to propel a 10.0-g steel ball. If the spring is compressed 7.00 cm and friction is negligible: (a) How much force is needed to compress the spring? (b) To what maximum height can the ball be shot? (c) At what angles above the horizontal may a child aim to hit a target 3.00 m away at the same height as the gun? (d) What is the gun's maximum range on level ground?

The common-gate transistor in Fig. earlier is biased at a drain current of $0.25 \mathrm{~mA}$ and is operating with an overdrive voltage $V_{O V}=0.25 \mathrm{~V}$. The transistor has an Early voltage $V_A$ of $5 \mathrm{~V}$. (a) Find $R_{\text {in }}$ for $R_L=\infty, 1 \mathrm{M} \Omega, 100 \mathrm{k} \Omega, 20 \mathrm{k} \Omega$, and 0 . (b) Find $R_o$ for $R_s=0,1 \mathrm{k} \Omega, 10 \mathrm{k} \Omega, 20 \mathrm{k} \Omega$, and $100 \mathrm{k} \Omega$.

Use the Newton-Raphson method to estimate a root of the equation

$$\cos x=x$$

You may start with $x_{0}=1$.

Write the following function. The call sum(g, 1, j) should returng(i) + ... +g (j).

int sum(int (*f)(int), int start, int end);

Brad grew $4 \frac{1}{4}$ inches this year and is now $56 \frac{7}{8}$ inches tall. Give and solve an equation to determine Brad's height at the start of the year. Show that your answer is reasonable.

What is diabetes? What causes diabetes and what effects does it have on the body? How is diabetes usually treated?