Additional Problems

| 60 | The punter on a football team tries to kick a football so that it stays in the air for a long “hang time.” If the ball is kicked with an initial velocity of 25.0 m/s at an angle of 60.0° above the ground, what is the “hang time”?

| 61 | A dolphin leaps out of the water at an angle of 35° above the horizontal. The horizontal component of the dolphin’s velocity is 7.7 m/s. Find the magnitude of the vertical component of the velocity.

| 62 | A bullet is fired from a rifle that is held 1.6 m above the ground in a horizontal position. The initial speed of the bullet is 1100 m/s. Find (a) the time it takes for the bullet to strike the ground and (b) the horizontal distance traveled by the bullet.

| 63 | ssm A golf ball rolls off a horizontal cliff with an initial speed of 11.4 m/s. The ball falls a vertical distance of 15.5 m into a lake below. (a) How much time does the ball spend in the air? (b) What is the speed v of the ball just before it strikes the water?

| 64 | Useful background for this problem can be found in Multiple-Concept Example 2. On a spacecraft two engines fire for a time of 565 s. One gives the craft an acceleration in the x direction of , while the other produces an acceleration in the y direction of . At the end of the firing period, the craft has velocity components of and . Find the magnitude and direction of the initial velocity. Express the direction as an angle with respect to the +x axis.

| 65 | ssm A fire hose ejects a stream of water at an angle of 35.0° above the horizontal. The water leaves the nozzle with a speed of 25.0 m/s. Assuming that the water behaves like a projectile, how far from a building should the fire hose be located to hit the highest possible fire?

| 66 | The perspective provided by Multiple-Concept Example 9 is useful here. The highest barrier that a projectile can clear is 13.5 m, when the projectile is launched at an angle of 15.0° above the horizontal. What is the projectile’s launch speed?

* | 67 | Before starting this problem consult Interactive Solution 3.67 at . A golfer, standing on a fairway, hits a shot to a green that is elevated 5.50 m above the point where she is standing. If the ball leaves her club with a velocity of 46.0 m/s at an angle of 35.0° above the ground, find the time that the ball is in the air before it hits the green.

* | 68 | Review Conceptual Example 5 and Concept Simulation 3.1 at before beginning this problem. You are traveling in a convertible with the top down. The car is moving at a constant velocity of 25 m/s, due east along flat ground. You throw a tomato straight upward at a speed of 11 m/s. How far has the car moved when you get a chance to catch the tomato?

* | 69 | ssm A small aircraft is headed due south with a speed of 57.8 m/s with respect to still air. Then, for a wind blows the plane so that it moves in a direction 45.0° west of south, even though the plane continues to point due south. The plane travels 81.0 km with respect to the ground in this time. Determine the velocity (magnitude and direction) of the wind with respect to the ground. Determine the directional angle relative to due south.

* | 70 | A person looking out the window of a stationary train notices that raindrops are falling vertically down at a speed of 5.0 m/s relative to the ground. When the train moves at a constant velocity, the raindrops make an angle of 25° when they move past the window, as the drawing shows. How fast is the train moving?

* | 71 | ssm www As preparation for this problem, review Conceptual Example 10. The two stones described there have identical initial speeds of and are thrown at an angle , one below the horizontal and one above the horizontal. What is the distance between the points where the stones strike the ground?

** | 72 | A jetliner can fly 6.00 hours on a full load of fuel. Without any wind it flies at a speed of . The plane is to make a round-trip by heading due west for a certain distance, turning around, and then heading due east for the return trip. During the entire flight, however, the plane encounters a 57.8-m/s wind from the jet stream, which blows from west to east. What is the maximum distance that the plane can travel due west and just be able to return home?

** | 73 | A placekicker is about to kick a field goal. The ball is 26.9 m from the goalpost. The ball is kicked with an initial velocity of 19.8 m/s at an angle above the ground. Between what two angles, and , will the ball clear the 2.74-m-high crossbar? (Hint: The following trigonometric identities may be useful: and .)

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