A ball is shot from the top of a building with an initial velocity of $24 \mathrm{~m} / \mathrm{s}$ at an angle $\theta=42^{\circ}$ above the horizontal. What are the horizontal and vertical components of the initial velocity?

A ball is shot from the top of a building with an initial velocity of 18 m/s at an angle $\theta=42^{\circ}$ above the horizontal. What are the x and y components of the initial velocity?

A boat, whose speed in still water is $2.80 \mathrm{~m} / \mathrm{s}$, must cross a $265-\mathrm{m}$---wide river and arrive at a point $118 \mathrm{~m}$ upstream from where it starts (Fig. 3-56). To do so, the pilot must head the boat at a $45.0^{\circ}$ upstream angle. What is the speed of the river's current?

An object, which is at the origin at time $t=0$, has initial velocity $\overrightarrow{\mathbf{v}}_0=(-14.0 \hat{\mathbf{i}}-7.0 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}$ and constant acceleration $\overrightarrow{\mathbf{a}}=(6.0 \hat{\mathbf{i}}+3.0 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}^2$. Determine the position $\overrightarrow{\mathbf{r}}$ where the object comes to rest (momentarily).

A smoke jumper jumps from a plane that is 1700 ft above the ground. The function $y=-16 t^{2}+1700$ gives the jumper's height y in feet at t seconds. a. How long is the jumper in free fall if the parachute opens at 1000 ft? b. How long is the jumper in free fall if the parachute opens at 940 ft?

A long jumper leaves the ground at $45^{\circ}$ above the horizontal and lands $8.0 \mathrm{~m}$ away. Now she is out on a hike and comes to the left bank of a river. There is no bridge and the right bank is $10.0 \mathrm{~m}$ away horizontally and $2.5 \mathrm{~m}$ vertically below. If she jumps from the edge of the left bank at $45^{\circ}$ with the speed calculated in (a), how long, or short, of the opposite bank will she land (Fig. 3-49)?

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

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?

Spymaster Andrea, flying a constant $208 \mathrm{~km} / \mathrm{h}$ horizontally in a low-flying helicopter, wants to drop secret documents into her contact's open car which is traveling $135 \mathrm{~km} / \mathrm{h}$ on a level highway $78.0 \mathrm{~m}$ below. At what angle (with the horizontal) should the car be in her sights when the packet is released (Fig. 3-60)?

A basketball is shot from an initial height of $2.40 \mathrm{~m}$ (Fig. 3-63) with an initial speed of $v_0=12 \mathrm{~m} / \mathrm{s}$ directed at an angle $\theta_0=35^{\circ}$ above the horizontal. How far from the basket was the player if he made a basket?

A basketball is shot from an initial height of $2.40 \mathrm{~m}$ (Fig. 3-63) with an initial speed of $v_0=12 \mathrm{~m} / \mathrm{s}$ directed at an angle $\theta_0=35^{\circ}$ above the horizontal. At what angle to the horizontal did the ball enter the basket?

A tiger leaps horizontally from a 6.5-m-high rock with a speed of 3.5 m/s. How far from the base of the rock will she land?

A batter hits a fly ball which leaves the bat $0.90 \mathrm{~m}$ above the ground at an angle of $64^{\circ}$ with an initial speed of $28 \mathrm{~m} / \mathrm{s}$ heading toward centerfield. Ignore the resistance of air. The ball is caught by the centerfielder who, starting at a distance of $105 \mathrm{~m}$ from home plate just as the ball was hit, runs straight toward home plate at a constant speed and makes the catch at ground level. Determine his speed.

A batter hits a fly ball which leaves the bat $0.90 \mathrm{~m}$ above the ground at an angle of $64^{\circ}$ with an initial speed of $28 \mathrm{~m} / \mathrm{s}$ heading toward centerfield. Ignore the resistance of air. How far from the home plate would the ball land if not caught?