- The ErgoBot is located at a position of (4, 8) m relative to the origin. It has been programmed to move in displacements of (15, 16) m and (23, 42) m. Where will it end up relative to the origin?
 What is the velocity of an object that travels 80 m north and 20 m west in 3 s?
- A plane can fly 100 m/s in still air with no wind. To what angle should the plane be steered if the pilot wants to head straight north in a crosswind that is blowing 10 m/s to the east?
- A rocket plane flying on a velocity vector of (0, 500, 0) m/s needs to turn to the east. How long must the plane maintain a sideways acceleration of (5, 0, 0) m/s2 before its velocity vector has moved 10° to the east?
- A baseball leaves the bat with a velocity of 55 m/s. The ballpark fence is 120 m away. Does the ball reach the fence if it leaves the bat traveling upward at an angle of 30º to the horizontal?
- The Empire State Building is 381 m tall.
- How long would it take for a marble to fall from the top of the Empire State Building to the ground, neglecting air friction.
- What initial velocity would you have to give the marble to make it hit the ground in 5 s?
- What initial velocity would you have to give the marble to make it hit the ground in 10 s?
- A volcano throws a stone 9,000 m into the air. What is the minimum initial velocity of the stone? In reality, air friction is significant and the actual velocity may be higher.
- What ramp angle would produce an acceleration of 2 m/s2 for a cart rolling down? Assume no friction and that the angle is measured with respect to the horizontal.
 A marble is shot horizontally from a tabletop with an initial speed of 2.5 m/s using a marble launcher. If the table is 0.8 m high, how far will the marble travel along the floor before it lands?
- A cart rolls down a 2.5 m frictionless ramp in 1.25 s after starting from rest at the top. What is the angle of the ramp?
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- If the coefficient of static friction is 0.35 for the ramp shown, at what angle should you set a ramp so the block just begins to slide down on its own?
- On your computer, use the interactive simulation of projectile motion on page 186 to determine the projection angle needed to hit a target 60 m away when the initial speed of the projectile is 25 m/s.
- Determine the tension in a rope used to tow a 90 kg skier up a 15° incline while accelerating the skier at 0.5 m/s2. The coefficient of kinetic friction is 0.2.
- A projectile can have the same range at different launch angles. Use the range equation to determine a different launch angle at which the calculated range is the same as it is for an angle of 53°. (Hint: 2 sin θ cos θ = sin 2θ.)
- A slippery plastic block is resting on a ramp that makes an angle of 20° with the horizontal. The coefficient of static friction between the block and the ramp is 0.2. The coefficient of kinetic friction is 0.15.
- Will the block start sliding on its own?
- If you found that the block slid in part a, calculate its acceleration. If not, then calculate the minimum angle the ramp must have to start the block sliding.
- A 4 kg car with frictionless wheels is on a ramp that makes a 25° angle with the horizontal. The car is connected to a 1 kg mass by a string that passes over a frictionless pulley.
- Draw a free-body diagram of the car.
- In which direction does the car move: up or down the ramp?
- Calculate the acceleration of the car and mass using Newton’s second law.
- A cyclist jumps off a low cliff at an initial velocity of 18 m/s. The cyclist travels 16.6 m before touching down. How high is the cliff?
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