A long jumper leaves the ground at $45^{\circ}$ above the horizontal and lands $8.0 \mathrm{~m}$ away. What is her "takeoff" speed $v_0$?

A 200 m wide river has a uniform flow speed of 1.1 m/s through a jungle and toward the east. An explorer wishes to leave a small clearing on the south bank and cross the river in a powerboat that moves at a constant speed of 5.0 m/s with respect to the water. There is a clearing on the north bank 82 m upstream from a point directly opposite the clearing on the south bank. (a) In what direction must the boat be pointed in order to travel in a straight line and land in the clearing on the north bank? (b) How long will the boat take to cross the river and land in the clearing?

In the mid-nineteenth century, explorers used the boiling point of water to estimate altitude. The boiling temperature of water T (in degrees F) can be approximated by the model T = -1.83a + 212, where a is the altitude in thousands of feet. (A) Determine the temperature at which water boils at an altitude of 4000 ft. Round to the nearest degree. (B) Two campers hiking in Colorado boil water for tea. If the water boils at 193 degrees F, approximate the altitude of the campers. Give the result to the nearest hundred feet.

The monthly profit for a small company that makes long-sleeve T-shirts depends on the price per shirt. If the price is too high, sales will drop. If the price is too low, the revenue brought in may not cover the cost to produce the shirts. After months of data collection, the sales team determines that the monthly profit is approximated by $f(p)=-50 p^{2}+1700 p-12,000,$ where p is the price per shirt and f(p) is the monthly profit based on that price. a. Find the price that generates the maximum profit. b. Find the maximum profit. c. Find the price(s) that would enable the company to break even.

Romeo is throwing pebbles gently up to Juliet's window, and he wants the pebbles to hit the window with only a horizontal component of velocity. He is standing at the edge of a rose garden $8.0 \mathrm{~m}$ below her window and $8.5 \mathrm{~m}$ from the base of the wall (Fig. 3-48). How fast are the pebbles going when they hit her window?

A swimmer is capable of swimming 0.45 m/s in still water. If she aims her body directly across a 75-m-wide river whose current is 0.40 m/s. How long will it take her to reach the other side?

A baseball is hit with a speed of $27.0 \mathrm{~m} / \mathrm{s}$ at an angle of $45.0^{\circ}$. It lands on the flat roof of a $13.0 \mathrm{~m}$ tall nearby building. If the ball was hit when it was $1.0 \mathrm{~m}$ above the ground, what horizontal distance does it travel before it lands on the building?

An airplane is heading due south at a speed of 600 km/h. If a wind begins blowing from the southwest at a speed of 100 km/h (average), calculate: the velocity (magnitude and direction) of the plane relative to the ground

What horizontal distance does the ball travel in this time?

At what projection angle will the range of a projectile equal its maximum height?

A baseball is hit with a speed of $27.0 \mathrm{~m} / \mathrm{s}$ at an angle of $45.0^{\circ}$. It lands on the flat roof of a $12.5\,\mathrm{m}$-tall nearby building. If the ball was hit when it was $1.2 \mathrm{~m}$ above the ground, what horizontal distance does it travel before it lands on the building?

A rescue plane wants to drop supplies to isolated mountain climbers on a rocky ridge $265 \mathrm{~m}$ below. If the plane is traveling horizontally with a speed of $125 \mathrm{~km} / \mathrm{h}$, how far in advance of the recipients (horizontal distance) must the goods be dropped?

An unmarked police car, traveling a constant $90$ km/h, is passed by a speeder traveling $140$ km/h. Precisely $1.00$ s after the speeder passes, the policeman steps on the accelerator. If the police car's acceleration is $2.00$ m/s$^2$, how much time elapses after the police car is passed until it overtakes the speeder (assumed moving at constant speed)?

A baseball is hit with a speed of $27.0 \mathrm{~m} / \mathrm{s}$ at an angle of $45.0^{\circ}$. It lands on the flat roof of a $13.0\ \mathrm{m}$-tall nearby building. If the ball was hit when it was $1.0 \mathrm{~m}$ above the ground, what horizontal distance does it travel before it lands on the building?