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

A rock is kicked horizontally at a speed of $15 \mathrm{~m} / \mathrm{s}$ from a hill with a $45^{\circ}$ slope (Fig. 3-65). How long does it take for the rock to hit the ground?

A hunter aims directly at a target (on the same level) $38.0 \mathrm{~m}$ away. At what angle should the bow be aimed so the target will be hit?

If a baseball pitch leaves the pitcher's hand horizontally at a velocity of $150 \mathrm{~km} / \mathrm{h}$, by what $\%$ will the pull of gravity change the magnitude of the velocity when the ball reaches the batter, $18 \mathrm{~m}$ away? For this estimate, ignore air resistance and spin on the ball.

When Babe Ruth hit a homer over the $8.0\,\text{m}$ high right-field fence $98 \mathrm{~m}$ from home plate, roughly what was the minimum speed of the baseball when it left the bat? Assume the ball was hit $1.0 \mathrm{~m}$ above the ground and its path initially made a $36^{\circ}$ angle with the ground.

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)?

Apollo astronauts took a "nine iron" to the Moon and hit a golf ball about $180$ m! Assuming that the swing, launch angle, and so on, were the same as on Earth where the same astronaut could hit it only $30$ m, estimate the acceleration due to gravity on the surface of the Moon. (Neglect air resistance in both cases, but on the Moon there is none!)

A diver running $2.3 \mathrm{~m} / \mathrm{s}$ dives out horizontally from the edge of a vertical cliff and $3.0 \mathrm{~s}$ later reaches the water below. How high was the cliff and how far from its base did the diver hit the water?

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 basketball is shot from a height of 8 feet at a horizontal distance of 15 feet from the basket. The initial speed is 27 ft/s and the initial angle is $30^{\circ}$ above the horizontal. The basket is at a height of 10 feet and extends from x=14.25' to x=15.75'. Show that the center of the ball goes through the basket.

A basketball is shot at a 70° angle with the horizontal direction with an initial speed of 10 m/sec. Find the component form of the initial velocity.

A car traveling $45$ km/h slows down at a constant $0.50$ m/s$^2$ just by "letting up on the gas." Calculate
(a) the distance the car coasts before it stops,

A child, who is $45 \mathrm{~m}$ from the bank of a river, is being carried helplessly downstream by the river's swift current of $1.0 \mathrm{~m} / \mathrm{s}$. As the child passes a lifeguard on the river's bank, the lifeguard starts swimming in a straight line until she reaches the child at a point downstream. If the lifeguard can swim at a speed of $2.0 \mathrm{~m} / \mathrm{s}$ relative to the water, how long does it take her to reach the child? How far downstream does the lifeguard intercept the child?