For the problem, draw a motion diagram, a force identification diagram, and a free-body diagram. A sprinter has just started a race and is speeding up as she runs down the track.

Andrea and Barsha are middle-distance runners for their school's track team. Andrea's time A in the 400-meter race on a randomly selected day is approximately Normally distributed with a mean of 62 seconds and a standard deviation of 0.8 second. Barsha's time B in the 400-meter race on a randomly selected day is approximately Normally distributed with a mean of 62.8 seconds and a standard deviation of 1 second. Assume that A and B are independent random variables. Find the probability that Barsha beats Ashley in the 400-meter race on a randomly selected day.

A restaurant orders spaghetti sauce in cylindrical metal cans. The volume of each can is about

$$160 \pi$$

cubic inches, and the height of the can is 6 inches more than the radius. Find the dimensions of the can.

For the problem, identify all the forces acting on the object and draw a free-body diagram of the object. A skydiver has his parachute open and is floating downward through the air at a constant speed.

Write general expressions for the electric and magnetic fields of a 1 GHz sinusoidal plane wave traveling in the +y direction in a lossless nonmagnetic medium with relative permittivity $\epsilon_{\mathrm{r}}=9$. The electric field is polarized along the x direction, its peak value is 6 V/m, and its intensity is 4 V/m at t=0 and y=2 cm.

If a car stops suddenly, you feel "thrown forward." We'd like to understand what happens to the passengers as a car stops. Imagine yourself sitting on a very slippery bench inside a car. This bench has no friction, no seat back, and there's nothing for you to hold on to. a. Draw a picture and identify all of the forces acting on you as the car travels in a straight line at a perfectly steady speed on level ground. b. Draw your free-body diagram. is there a net force on you? If so, in which direction? c. Repeat parts a and b with the car slowing down. d. Describe what happens to you as the car slows down. e. Use Newton's laws to explain why you seem to be "thrown forward" as the car stops. Is there really a force pushing you forward?

Dave pushes his four-year-old son Thomas across the snow on a sled. As Dave pushes, Thomas speeds up. Which statement is true? A. The force of Dave on Thomas is larger than the force of Thomas on Dave. B. The force of Thomas on Dave is larger than the force of Dave on Thomas. C. Both forces have the same magnitude. D. It depends on how hard Dave pushes on Thomas.

For the problem, identify all the forces acting on the object and draw a free-body diagram of the object. A box is being dragged across the floor at a constant speed by a rope pulling horizontally on it. Friction is not negligible.

A car is driven east for a distance of 50 km, then north for 30 km, and then in a direction 30° east of north for 25 km. Sketch the vector diagram and determine (a) the magnitude and (b) the angle of the car’s total displacement from its starting point.

(a) Justify the formulas $\cos \theta=\left(e^{j \theta}+e^{-j \theta}\right) / 2$ and $\sin \theta=\left(e^{i \theta}-e^{-i \theta}\right) / 2 j$, using the appropriate series. (b) Display the above relationships geometrically by means of vector diagrams in the xy plane.

For the problem. Draw a motion diagram, a force identification diagram, and a free-body diagram. You've slammed on the brakes and your car is skidding to a stop while going down a $20 ^ { \circ }$ hill.

If you are standing still, the upward normal force on you from the floor is equal in magnitude to the weight force that acts on you. But it's possible to move so that the normal force is greater than your weight. Explain how this could be done.

For the problem, draw a motion diagram, a force identification diagram, and a free body diagram. A spring-loaded gun shoots a plastic ball. The trigger has just been pulled and the ball is starting to move down the barrel. The barrel is horizontal.

Use universal instantiation or universal modus ponens to fill in valid conclusions for the arguments.

$$\forall$$

real numbers r , a, and b, if r is positive, then

$$\left( r ^ { a } \right) ^ { b } = r ^ { a b }$$

. r=3, a =1/2, and b=6 are particular real numbers such that r is positive.

$$\therefore$$

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