A rocket designed to place small payloads into orbit is carried to an altitude of 12.0 km above sea level by a converted airliner. When the airliner is flying in a straight line at a constant speed of 850 km/h, the rocket is dropped. After the drop, the airliner maintains the same altitude and speed and continues to fly in a straight line. The rocket falls for a brief time, after which its rocket motor turns on. Once that motor is on, the combined effects of thrust and gravity give the rocket a constant acceleration of magnitude 3.00g directed at an angle of 30.0° above the horizontal. For safety, the rocket should be at least 1.00 km in front of the airliner when it climbs through the airliner's altitude. Your job is to determine the minimum time that the rocket must fall before its engine starts. Ignore air resistance. Your answer should include (a) a diagram showing the flight paths of both the rocket and the airliner, labeled at several points with vectors for their velocities and accelerations; (b) an x – t graph showing the motions of both the rocket and the airliner; and (c) a y – t graph showing the motions of both the rocket and the airliner. In the diagram and the graphs, indicate when the rocket is dropped, when the rocket motor turns on, and when the rocket climbs through the altitude of the airliner.

A hot-air balloon is rising upward with a speed of 15.5 m/s at an angle of 32.8° with respect to the horizontal.  A rock is released from rest relative to the balloon when it is 938.9 m above the ground.  How much time elapses before the rock hits the ground?

You want to know the height of a cliff so you throw a rock off the edge with an initial speed of 24.7 m/s inclined at an angle 31.2° above the horizontal. You have a friend that records that it takes 4.6 s for the rock to hit the bottom of the canyon after it is thrown. For the following questions, call up the positive y direction and make the positive x direction horizontal and towards the direction the rock is thrown. If you ignore air resistance, what is the y component of the velocity of the rock right before it hits the ground?

In a video game, a science-fictional “angry bird” is launched straight upwards by a high-velocity cannon from the surface of a planet far from Earth. The bird’s initial vertical velocity is 249 m/s (up). Ifgravity around this planet is a constant 11.2 m/s2, and the video game does kinematics correctly,how much time does it take the bird to reach the top if its trajectory?

For this problem, you can think of the jet stream as a river of air. Across the United States, the jet stream usually moves from west to east. We will assume that the jet stream is moving in its usual direction at 9.00 x 101 km/hr. On a particular day, you need to pilot a plane from one city to another that is 4.50 x 102 km directly to the south. The top speed of the aircraft in still air is 285 km/hr. (a) Make a sketch to represent what is happening in this problem. Label all quantities that you know. (b) Using cardinal directions (north, east, south, west) to give a heading, which direction should you aim the plane to reach the city directly to the south at top speed? (c) How fast (in km/hr) would you be moving relative to the ground? (c) How much time (in hr) will it take you to reach your destination?

A space vehicle is coasting at a constant velocity of 24.6 m/s in the +y direction relative to a space station. The pilot of the vehicle fires a RCS (reaction control system) thruster, which causes it to accelerate at 0.201 m/s² in the +x direction. After 47.8 s, the pilot shuts off the RCS thruster. After the RCS thruster is turned off, find (a) the magnitude and (b) the direction of the vehicle's velocity relative to the space station. Express the direction as an angle (in degrees) measured from the +y direction. (a) Number i (b) Number i Units Units +

In the winter sport of bobsledding, athletes push their sled along a horizontal ice surface and then hop on the sled as it starts to careen down the steeply sloped track. In one event, the sled reaches a top speed of 9.2 m/sm/s before starting down the initial part of the track, which is sloped downward at an angle of 5.0 degrees. What is the sled's speed after it has traveled the first 140 m?

On a beautiful spring day, Juan is playing a round of golf. He hits the golfball with an initial velocity of 37 m/s at an angle of 27.4°. If it hits the ground 5.8s later, how far does it travel? Ignore air resistance. Answer: m