A high-performance jet plane, practicing radar avoidance maneuvers, is in horizontal flight 45.0 m above the level ground. Suddenly, the plane encounters terrain that slopes gently upward at 3.50°, an amount difficult to detect (see the figure). How much time does the pilot have to make a correction to avoid flying into the ground ( s)? The speed of the plane is 1150 km/h.

A stone is thrown horizontally from the highest point of a 95 m building and lands 115 m from the base of the building. Ignore air resistance, and use a coordinate system whose origin is at the highest point of the building, with positive y upwards and positive x in the direction of the throw. How long is the stone in the air in seconds? What must have been the initial horizontal component of the velocity, in meters per second? What is the vertical component of the velocity just before the stone hits the ground, in meters per second? What is the magnitude of the velocity of the stone just before it hits the ground, in meters per second?

A daredevil drove his motorcycle up an incline at 30 degree angle with the horizontal and got air borne at the end of the incline at 20 m/s, 11 m above the ground. How far horizontally did he land with his motorcycle on the ground, on a safety net?

A skater is gliding along the ice at 2.2 m/s, when she undergoes an acceleration of magnitude 1.2 m/s2 for 3.0 s. At the end of that time she is moving at 5.8 m/s. (a) What must be the angle between the acceleration vector and the initial velocity vector?

*Draw a simple diagram representation for the solution.In a game war, one team sets base on a cliff 15m high and 60m away from the opponent’s base. At what velocity must the attack be launched so that the lower base will be hit? The initial launch is at 20 degrees below the horizontal?

a ball is launched with a velocity of magnitude 10.0 m/s, at an angle of 50.0° to the horizontal.The launch point is at the base of a ramp of horizontal length d1 6.00 m and height d2 = 3.60 m. A plateau is located at the top of the ramp. (a) Does the ball land on the ramp or the plateau? When it lands, what are the (b) magnitude and (c) angle of its displacement from the launch point?

Consider a projectile launched form ground level at an angle of elevation with an initial velocity . The maximum horizontal range is given by xmax=(v 2/0 sin2θ)/g, where g is the acceleration due to gravity. Here is the problem: If a soccer ball is kicked from ground level with an initial velocity of 28 m/sec, what is the smallest positive angle at which the player should kick the ball to reach a teammate 48m down the field? Assume that the ball reaches the teammate at ground level on the fly. Round to the nearest tenth of a degree.

An inflatable life raft is released from an airplane at 300 m altitude, in level flight, with an air speed of 100 m/s in the horizontal direction. At what horizontal distance from the release point does the raft strike the water?

A flock of ducks is trying to migrate south for the winter, but they keep being blown off course by a wind blowing from the west at 12 m/s. A wise elder duck finally realizes that the solution is to fly at an angle to the wind. If the ducks can fly at 16 m/s relative to the air, in what direction should they head in order to move directly south?

A cannon launches a cannonball from level ground with an initial speed of 80 m/s at an angle of 280 above the horizontal. What horizontal distance does the cannonball travel when the cannonball returns to the ground? Given the same initial velocity of launch, at what other angle above the ground can the cannonball be fired and achieve the same horizontal range as before? (Assume that g = 9.81 m/s2.)   a. Range = 540 m, and angle = 420 above the horizontal   b. Range = 600 m, and angle = 620 above the horizontal   c. Range = 270 m, and angle = 620 above the horizontal   d. Range = 540 m, and angle = 620 above the horizontal   e. Range = 270 m, angle = 420 above the horizontal