A mountain climber jumps a crevasse of width $W$ by leaping horizontally with speed $v_0$. If the height difference between the two sides of the crevasse is $h$, what is the minimum value of $v_0$ for the climber to land safely on the other side?

(a) What were some beliefs of the Quakers? (b) How did these beliefs influence William Penn's "holy experiment"?

Fill in the blanks to complete the recursive formula that corresponds to the sequence shown. 14, 23, 32, 41, 50, .... a __= ____ + ____ n

In this problem find horizontally shifted sine and cosine functions so that each function satisfies the given conditions. Graph the functions.

Amplitude $\frac{5}{4}$, period 4 , shifted by $1 / 2 \pi$ units to the left.

A football is thrown with an initial upward velocity component of $15.0 \mathrm{~m} / \mathrm{s}$ and a horizontal velocity component of $18.0 \mathrm{~m} / \mathrm{s}$.
(a) How much time is required for the football to reach the highest point in its trajectory?
(b) How high does it get above its release point?
(c) How much time after it is thrown does it take to return to its original height? How does this time compare with what you calculated in part (b)? Is your answer reasonable?
(d) How far has the football traveled horizontally from its original position?

A rope of negligible mass is stretched horizontally between two supports that are 3.44 m apart. When an object of weight 3160 N is hung at the center of the rope, the rope is observed to sag by 35.0 cm. What is the tension in the rope?

For the following exercises, write a formula for the function g that results when the graph of a given toolkit function is transformed as described. The graph of $f(x)=x^{2}$ is horizontally stretched by a factor of 3, then shifted to the left 4 units and down 3 units.

i) Write an equation for the function that results from each set of transformations. ii) State the domain and range. For even functions, state the vertex and the equation of the axis of symmetry. a) $f(x)=x^{4}$ is compressed vertically by a factor of $\frac{3}{5}$, stretched horizontally by a factor of 2, reflected in the y-axis, and translated 1 unit up and 4 units to the left. b) $f(x)=x^{3}$ is compressed horizontally by a factor of $\frac{1}{4}$, stretched vertically by a factor of 5, reflected in the x-axis, and translated 2 units to the left and 7 units up.

Choose the best answer.

If $y=\sqrt{x}$ is stretched horizontally by a factor of 6, which function results?

A $y=\frac{1}{6}\sqrt{x}$

B $y=6\sqrt{x}$

C $y=\sqrt{\frac{1}{6}x}$

D $y=\sqrt{6x}$

A horizontal force of $18\ \mathrm{lb}$ is required to just start a $45-\mathrm{lb}$ block in motion on a horizontal surface. Determine the coefficient of static friction between the block and the supporting surface.

The hang time of a basketball player who jumps a vertical distance of 2 ft (0.6 m) is about 0.6 s. What is the hang time if the player reaches the same height while jumping 4 ft (1.2 m) horizontally?

A rookie quarterback throws a football with an initial upward velocity component of $16.0 \mathrm{~m} / \mathrm{s}$ and a horizontal velocity component of $20.0 \mathrm{~m} / \mathrm{s}$. Ignore air resistance. (a) How much time is required for the football to reach the highest point of the trajectory? (b) How high is this point? (c) How much time (after it is thrown) is required for the football to return to its original level? How does this compare with the time calculated in part (a)? (d) How far has the football traveled horizontally during this time? (e) Draw $x-t$, $y-t, v_x-t$, and $v_y-t$ graphs for the motion.

A mountain climber jumps a crevasse of width $W$ by leaping horizontally with speed $v_0$. If the height difference between the two sides of the crevasse is $h$, what is the minimum value of $v_0$ for the climber to land safely on the other side?

A golfer launches a tee shot down a horizontal fairway; it follows a path given by $r(t)=\left\langle a t , ( 75 - 0.1 a ) t , - 5 t ^ { 2 } + 80 t \right\rangle$, where $t \geq 0$ measures time in seconds and r has units of feet. The y-axis points straight down the fairway and the z-axis points vertically upward. The parameter a is the slice factor that determines how much the shot deviates from a straight path down the fairway.

With a slice (a=0.2), sketch and describe the shot. How far does the ball travel horizontally?