A rock is on an inclined surface. The rock is originally at rest, but starts to slide down the incline. The magnitude of the force on the surface due to the rock is $F_{SR}$ , and the magnitude of the force on the rock due to the surface is $F_{RS}$. If we com- pare these forces, we find
$(A)$ $F_{SR}<F_{RS}$. always. $(B)$ $F_{SR}=F_{RS}$ when the rock is at rest but then $F_{SR}>F_{RS}$. $(C)$ $F_{SR}=F_{RS}$ always. $(D)$ $F_{SR}>F_{RS}$ always.

A particle leaves the origin with an initial velocity

$${\overrightarrow{v}} = (3.00{\hat{i}}) \ m/s$$

and a constant acceleration

$${\overrightarrow{a}} = (-1.00{\hat{i}} - 0.500{\hat{j}}) \ m/s^2$$

. When it reaches its maximum x coordinate, what are its (a) velocity and (b) position vector?

Change this verb from the present tense to the preterite tense.

1. Ustedes lavan

Of the objects listed in earlier Table, which might be considered as a particle for the motion described? For those that behave like particles, can you describe a type of motion in which they could $\it{not}$ be considered as particles?

A football kicker can give the ball an initial speed of 25 m/s. What are the (a) least and (b) greatest elevation angles at which he can kick the ball to score a field goal from a point 50 m in front of goalposts whose horizontal bar is 3.44 m above the ground?

A $10.0$ kg object is launched vertically into the air with an initial velocity of $50.0$ m/s. In addition to the force of gravity there is a frictional force which is proportional to velocity ac- cording to $f_y=-bv_y$; note that this frictional force is nega- tive (down) when the object is moving up, but positive (up) when the object is moving down. (a) Numerically generate distance-time graphs for the object, using $b=0$, but use several different step sizes for $\Delta$ $t$, such as $1.0$ s, $0.1$ s, $0.01$ s, and $0.001$ s. Show the results on a sin- gle graph. How does the highest point vary with the step size? (b) Numerically generate distance-time graphs for the object, using a step size of $\Delta$ $t=0.01$ s. Now, however, try non-zero values for $b$, such as $0.1~\mathrm{N}~\cdot$ s/m, $0.5~\mathrm{N}~\cdot$ s/m, $1.0~\mathrm{N}~\cdot$ s/m, $5.0~\mathrm{N}~\cdot$ s/m and $10.0~\mathrm{N}~\cdot$ s/m. How does the highest point vary with $b?$ What do you notice about the shape of the graphs as $b$ increases?

A radio station advertises that it is “at $89.5$ on your FM dial.” What does this number mean?

Determine the limit of the sequence or show that the sequence diverges by using the appropriate Limit Laws or theorems.

$$a_n=\sqrt[n]{n}$$

Suppose that the Sun’s gravitational force was suddenly turned off, so that Earth became a free object rather than be- ing confined to orbit the Sun. How long would it take for Earth to reach a distance from the Sun equal to Pluto’s pres- ent orbital radius? (Hint: You will find some of the data you need in earlier Appendix.)

An interstellar spacecraft, far from the influence of any stars or planets, is moving at high speed under the influence of fu- sion rockets when the engines malfunction and stop. The spacecraft will
$(A)$ immediately stop, throwing all of the occupants to the front of the craft. $(B)$ begin slowing down, eventually coming to a rest in the cold emptiness of space. $(C)$ keep moving at constant speed for a while, but then be- gin to slow down. $(D)$ keep moving forever at the same speed.

Use calculus to find the area of the triangle with the given vertices. (0,0), (3,1), (1,2)

A spherical conducting ball is suspended by an insulating thread. A positive point charge is moved near the ball. The ball will (A) be attracted to the point charge and swing toward it. (B) be repelled from the point charge and swing away from it. (C) not be affected by the point charge.

A spherical conducting ball is suspended by an insulating thread. A positive point charge is moved near the ball. The ball will (A) be attracted to the point charge and swing toward it. (B) be repelled from the point charge and swing away from it. (C) not be affected by the point charge.

Suppose that the Sun’s gravitational force was suddenly turned off, so that Earth became a free object rather than be- ing confined to orbit the Sun. How long would it take for Earth to reach a distance from the Sun equal to Pluto’s pres- ent orbital radius? (Hint: You will find some of the data you need in earlier Appendix.)