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)?

You buy a plastic dart gun, and being a clever physics student you decide to do a quick calculation to find its maximum horizontal range. You shoot the gun straight up, and it takes 4.0 s for the dart to land back at the barrel. What is the maximum horizontal range of your gun?

At $t=0$ a batter hits a baseball with an initial speed of $28 \mathrm{~m} / \mathrm{s}$ at a $55^{\circ}$ angle to the horizontal. An outfielder is $85 \mathrm{~m}$ from the batter at $t=0$ and, as seen from home plate, the line of sight to the outfielder makes a horizontal angle of $22^{\circ}$ with the plane in which the ball moves (see Fig. 3-66). What speed and direction must the fielder take to catch the ball at the same height from which it was struck? Provide the angle with respect to the outfielder's line of sight to home plate.

The speed of a boat in still water is v. The boat is to make a round trip in a river whose current travels at speed u. Derive a formula for the time needed to make a round trip of total distance D if the boat makes the round trip by moving directly across the river and back. We must assume u<v; why?

The speed of a boat in still water is $v$. The boat is to make a round-trip in a river whose current travels at speed $u$. Derive a formula for the time needed to make a round trip of total distance $D$ if the boat makes the round-trip by moving (a) upstream and back downstream, (b) directly across the river and back. We must assume $u<v$; why?

The speed of a boat in still water is v. The boat is to make a round trip in a river whose current travels at speed u. Derive a formula for the time needed to make a round trip of total distance D if the boat makes the round trip by moving upstream and back downstream; why?

At serve, a tennis player aims to hit the ball horizontally. What minimum speed is required for the ball to clear the $0.90$-m-high net about $15.0 \mathrm{~m}$ from the server if the ball is "launched" from a height of $2.30 \mathrm{~m}$ ? Where will the ball land if it just clears the net (and will it be "good" in the sense that it lands within $7.0 \mathrm{~m}$ of the net)? How long will it be in the air? See Fig. 3-50.

A grasshopper hops along a level road. On each hop, the grasshopper launches itself at angle $\theta_0=45^{\circ}$ and achieves a range $R=0.80 \mathrm{~m}$. What is the average horizontal speed of the grasshopper as it hops along the road? Assume that the time spent on the ground between hops is negligible.

An Olympic long jumper is capable of jumping 8.0 m Assuming his horizontal speed is 9.1 m/s as he leaves the ground, how long is he in the air and how high does he go? Assume that he lands standing upright-that is, the same way he left the ground.

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 $725 \mathrm{~m}$. After this point, its acceleration is that of gravity, downward. With what velocity does it 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 $725 \mathrm{~m}$. After this point, its acceleration is that of gravity, downward. How long (total) is it in the air?

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 $775 \mathrm{~m}$. After this point, its acceleration is that of gravity, downward. $(a)$ What is the velocity of the rocket when it runs out of fuel? $(b)$ How long does it take to reach this point? $(c)$ What maximum altitude does the rocket reach? $(d)$ How much time (total) does it take to reach maximum altitude? $(e)$ With what velocity does it strike the Earth? $(f)$ How long (total) is it in the air?

An elevator (mass $4850$ kg) is to be designed so that the maximum acceleration is $0.0600$ g. What are the maximum and minimum forces the motor should exert on the supporting cable?

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 $725 \mathrm{~m}$. After this point, its acceleration is that of gravity, downward. How much time (total) does it take to reach maximum altitude?