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?

The maximum height $H$ in feet that a basketball reaches after being shot is given by the formula $H=\frac{V_0^2(\sin \theta)^2}{64}$, where $V_0$ represents the initial velocity in feet per second, $\theta$ represents the degree measure of the angle that the path of the basketball makes with the ground. Find the maximum height reached by a ball shot with an initial velocity of 30 feet per second at an angle of $70^{\circ}$.

A stone is thrown vertically upward with a speed of $15.5 \mathrm{~m} / \mathrm{s}$ from the edge of a cliff $75.0 \mathrm{~m}$ high (Fig. 2-47). What is its speed just before hitting?

In the aerials competition in skiing , the competitors speed down a ramp that slopes sharply upward at the end . The sharp upward slope launches them into the air, where they perform acrobatic maneuvers. The end of a launch ramp is directed $63^{\circ}$ above the horizontal. With this launch angle , a skier attains a height of 13 m above the end of the ramp. What is the skier's launch speed?

A rocket rises vertically, from rest, with an acceleration of $3.2 \mathrm{m} / \mathrm{s}^{2}$ until it runs out of fuel at an altitude of 1200 m. After this point, its acceleration is that of gravity, downward. With what velocity does the rocket strike the Earth?

A rocket rises vertically, from rest, with an acceleration of $3.2 \mathrm{m} / \mathrm{s}^{2}$ until it runs out of fuel at an altitude of 1200 m. After this point, its acceleration is that of gravity, downward. What maximum altitude does the rocket reach?

A stone is dropped from the top of a cliff. It is seen to hit the ground below after $3.50$ s. How high is the cliff?

In coming to a stop, a car leaves skid marks $65 \mathrm{~m}$ long on the highway. Assuming a deceleration of $4.00 \mathrm{~m} / \mathrm{s}^2$, estimate the speed of the car just before braking.

A projectile is launched from ground level to the top of a cliff which is $195 \mathrm{~m}$ away and $135 \mathrm{~m}$ high (see Fig. 3-62). If the projectile lands on top of the cliff $6.6 \mathrm{~s}$ after it is fired, find the initial velocity of the projectile (magnitude and direction). Neglect resistance of air.

A projectile is launched from ground level to the top of a cliff which is 195 m away and 155 m high. If the projectile lands on top of the cliff 7.6 s after it is fired, find the initial velocity of the projectile (magnitude and direction). Neglect air resistance.

A diver running $2.5 \mathrm{~m} / \mathrm{s}$ dives out horizontally from the edge of a vertical cliff and $3.5 \mathrm{~s}$ later reaches the water below. How high was the cliff and how far from its base did the diver hit the water?

You are lying on a beach, your eyes $20 \mathrm{~cm}$ above the sand. Just as the Sun sets, fully disappearing over the horizon, you immediately jump up, your eyes now $150 \mathrm{~cm}$ above the sand, and you can again just see the top of the Sun. If you count the number of seconds $(=t)$ until the Sun fully disappears again, you can estimate the Earth's radius. But for this Problem, use the known radius of the Earth to calculate the time $t$.

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,

One 3.2-kg paint bucket is hanging by a massless cord from another 3.2-kg paint bucket, also hanging by a massless cord. If the buckets are at rest, what is the tension in each cord?