. A beanbag is thrown from a window located 10.0 m above the ground with an initial horizontal velocity of 3.0 m/s. a. How long will it take the beanbag to reach the ground? That is, what is its time of flight? b. How far will the beanbag travel horizontally? That is, what is its range? . Assuming there is no air resistance, at what angle should you launch a projectile from the ground so that it has the: a. greatest time of flight? b. greatest range? . A soccer player running on a level playing field kicks a soccer ball with a velocity of 9.4 m/s at an angle of 40 above the horizontal. Determine the soccer ball's: a. time of flight b. range 0. maximum height . What happens to the (i) range, (ii) maximum height, and (iii) time of flight when the initial velocity of a projectile is doubled (i.e. v = 2)? Assume the projectile lands at the same height from which it was launched. . A rock is thrown from the edge of a cliff 30 m high with an initial velocity of 20 m/s directed 50" above the horizontal. a. What are the rock's initial velocity components? b. How far from the base of the cliff does the rock land? '2 c. Which person applies the greater vertical force to the load? d. What effect does this have on frictional forces? On the vertical motion of the load? 5 1. 2. 3. Explain why an airplane moving through the air is not an example of projectile motion. A stone is thrown horizontally under negligible air resistance. 1What are its ver- tical acceleration and its horizontal acceleration? A marble rolls off a table with a velocity of 1.03 mfs [horizontally}.The tabletop is F05 cm above the floor. If air resistance is negligible, determine [a] how long the marble is airborne [b] the horizontal range [c] the velocity at impact . A stone is thrown horizontally with an initial speed of 0.0 mz's from a cliff. Air resistance is negligible. [a] Determine the horizontal and vertical components of displacement and instantaneous velocity at t = 0.0 s, 1.0 s, 2.0 s. and 3.0 s. [b] Draw a scale diagram showing the path of the stone. [c] Draw the instantaneous velocity vector at each point on your diagram. [d] Determine the average acceleration between 1.0 s and 2.0 s, and between 2.0 s and 3.0 s. Itiv'hat do you conclude? 2 Understanding Concepts 3. The force of gravity on a textbook is 18 N [down]. 1. You push your ruler westward at a constant speed across (a) What is the net force on the book if it is held stationary your desk by applying a force at an angle of 250 above the in your hand? horizontal. (b) Neglecting air resistance, what is the net force acting (a) Name all the forces acting on the ruler and state which on the book if you suddenly remove your hand? ones are contact forces. 4. At one particular instant in its flight, a ball experiences a (b) What fundamental force is responsible for the contact gravitational force . - 15 N [down] and an air resistance forces? force Fair = 0.50 N [32 above the horizontal] Calculate the (c) Draw an FBD of the ruler in this situation. Where net force on the ball. appropriate, include the components of forces. 5.) Given the following force vectors, FA = 3.6 N [28 W of S], 2. Draw an FBD for objects H, I, J, and K. FR = 4.3 N [15. N of W], and Fc = 2.1 N [24 E of S], (a) a cup (H) hanging from a hook determine (b) a person (I) standing in an elevator that is moving (a) FA + FB + Fc, using a vector scale diagram downward (b) FA + FB + Fc, using components (c) a curling rock (J) sliding freely in a straight line (c) FA - FB, using a vector scale diagram on a rink (d) FA - FB, using trigonometry 5 (d) a crate (K)being dragged acros floor, with signifi-An object with a mass of 15 kg rests on a frictionless horizontal plane and is acted upon by a horizontal force of 30 N. What will be its velocity after 10 s? A car with a mass of 1000 kg is moving in a straight line at a constant speed of 30 ms when the driver applies the brakes and brings the car to rest in 25 s. What constant force is acting to stop the car? Two children are playing with a wagon. One child pulls forward on a rope tied to the front, while the other child pushes on the wagon from behind. Draw a FBD showing all the forces acting on the wagon? Be sure to label the forces accordingly. (Hint: there are five forces in total) A 0.17 kg hockey puck slides along the ice at 19 m/s[E] when it hits a rough patch of ice that is 5.1 m across. Assume the coefcient of kinetic friction (pk) between the puck and the rough ice is 0.47. a. Draw a FBD of the puck moving on the rough ice. b. Calculate the kinetic friction acting on the puck. c. Determine the puck's average acceleration while on the rough ice. d. Calculate the puck's velocity as it leaves the rough ice and returns to the smooth ice. 5. To move a 45 kg wooden crate across a wooden floor (p = 0.20), a worker ties a rope onto the crate and pulls on the rope with a force of 115 N. a. Draw FBD of the situation. b. Resolve Fa into its component forces and determine their values. c. How much time elapses before the crate is moving at 1.4 m/s? 6. Two people pull on an object at different angles but with equal force a. Which person applies the greater horizontal force to the load? (Hint: if no measurements are given in a problem you may want to assume some. In this case, assume a force of 100 N and angles of 30 and 60 respectively.) b. What effect does this have on the horizontal motion of the load? 5 1. A cruise ship is moving with a velocity of 2.8 m/s[fwd] relative to the water. A group of tourists walks on the deck with a velocity of 1.1 m/s relative to the deck. Determine the velocity of the tourists relative to the water (vm) if they are walking toward: a. the bow (i.e. the front of the ship) b. the stern (i.e. the rear of the ship) c. the starboard (is. the right side of the ship as you face the bow) 2. A canoeist, capable of travelling at a speed of4.5 m/s in still water, is crossing a river that is owing with a velocity of 3.2 m/s[E]. The river is 220 m wide. a. If the canoe is aimed northward, what is the velocity of the canoe relative to the shore? b. How long does it take the canoe to cross the river? c. How far downstream does the canoe land? d. If the canoeist wanted to land directly across from the starting position, at what angle should the canoe be aimed? 3. An airplane flies due north over Sudbury with a velocity relative to the air of 235 km/h and with a wind velocity of 65.0 km/h[NE]. Calculate the speed and direction of the airplane. 1. (a) As the altitude of an Earth satellite in circular orbit increases, does the speed of the satellite increase, decrease, or remain the same? Why? (b) Check your answer by comparing the speed of the HST (discussed in Sample Problem 1) with the speed of the Moon. The orbital radius of the Moon is 3.84 X 105 km. 2. The ISS follows an orbit that is, on average, 450 km above the surface of Earth. Determine (a) the speed of ISS and (b) the time for one orbit. 3. Derive an expression for the radius of a satellite's orbit around Earth in terms of the period of revolution, the universal gravitation constant, and Earth's mass. 4. Satellite-broadcast television is an alternative to cable. A "digital TV" satellite fol- lows a geosynchronous orbit. (a) State the period of revolution of the satellite in seconds. (b) Determine the altitude of the orbit above the surface of Earth