Physics 1100 In-Class Problems: 2D Kinematics

Constant Velocity, Distance and Time



1. In a flat desert, two vehicles are initially together but head off at constant velocity in different directions. Vehicle A heads off at 50 km/h at 30° west of north while vehicle B heads due East at 45 km/h. In two hours, each stops. How far away, and in which direction, is vehicle B away from A?


2. In a flat desert, two vehicles are initially together but head off at constant velocity in different directions. Vehicle A heads off at 50 km/h at 30° west of north while vehicle B heads due East at an unknown speed. Ninety minutes later both stop. Vehicle A now is 190 km away from vehicle B at 20° north of west. How fast was B moving?


3. In a flat desert, two vehicles are initially together but head off at constant velocity in different directions. Vehicle A heads off at unknown speed at 30° west of north while vehicle B heads due East at 50 km/h. One hour later both stop. Vehicle A now is 95.4 km away from vehicle B at 33° north of west. How fast was A moving?


4. A speedboat is travelling at 25 km/h at 25° west of north relative to a river.  The river is travelling at 8.0 km/h at 15° south of east relative to the earth.  What is the speed of the boat relative to a person on the bank of the river?


5. A captain has his ship moving on the ocean at 12.0 knots at 22.0° west of north . The coast guard office tells him that shore radar indicates he is travelling at 13.2 knots at 28.5° west of north. What is the speed and direction of the ocean current at the ship’s location?


6. An airplane moves with a speed of 420 km/h with respect to the air at an angle of 20.0° west of north.  Find the velocity of the plane relative to the ground if the air (i.e. the wind) is moving at:
   1. 25.0 km/h due north.
   2. 17.8 km/h at 37.0° east of south.


7. An airplane pilot sets a compass course due west and maintains an airspeed of 240 km/h. An hour later, she finds herself over a town which is 290 km west and 35 km north of her starting point.
   1. Find the pilot's actual speed relative to the ground.
   2. Determine the magnitude and direction of the wind's velocity.


8. A 100-m wide river flows from west to east at 2.00 m/s.  A boat moves at 4.00 m/s due north relative to the water. Where on the north bank will the boat land? How long does it take the boat to get there?


9. A 100-m wide river flows from west to east at 2.00 m/s. A boat moves at 4.00 m/s relative to the water. If a person in a boat wishes to cross from the south bank directly over to the north bank, in which direction must the person head? How long would it take? Where would she land on the north bank?


10. A pilot is trying to fly to a town 350 km due east of where he is. A wind is blowing due north at 50 km/h. The plane can fly at 250 km/h with respect to the air. Which way must the pilot head to reach his destination? How long will the trip take?


11. Ship A is 100 km due west of ship B. Ship A is travelling at 15.0 km/h at 40.0° north of east. Ship B is travelling at 12 km/h at 53.5° north of west.
    1. Will the two ships collide? How can you tell?
    2. If they do, when will this occur?


12. A submarine, waiting in ambush, detects an enemy destroyer 10 km east and 6 km south of its position travelling at 15 km/h at 30° west of north. The sub is pointing due east. Its torpedoes travel at 30 km/h. When should it fire its torpedoes to hit the destroyer?

Nonconstant velocity



13. A ball has an initial velocity of 30 m/s at an angle of 30.0° above the horizontal and experiences a constant acceleration of 10.0 m/s² at 45.0° above the horizontal. What is the particle's displacement and velocity 5.00 s later?


14. A rocket has an initial velocity of 15.0 m/s at 22.0° above the horizontal. Fifteen seconds later, it has a velocity of 25.0 m/s at 42.0° above the horizontal. Find the magnitude and direction of the acceleration. Find the displacement in the x and y directions. Assume that the acceleration is constant.

Projectiles



15. A muscular boy and a puny boy of equal height are standing on a cliff 120 m above the ocean. Both throw a rock horizontally out off the cliff at the same time. The muscular boy can throw a rock four times as far as the puny boy. Which boy's rock hits the water first? How long is each boy's rock in the air? If the puny boy's rock hits the water 15.0 m from the base of the cliff, how fast does the muscular boy throw his rock? What is the magnitude and direction of the velocity of each boy's rock just before it hits the water? Sketch the motion.


16. You are trapped on the top of a burning building. Death is imminent and help is nowhere in sight. There is a safe building 6.50 m away and 3.00 m lower. You decide to try and make it across. You run horizontally off your building at 8.10 m/s. Do you make it across? If you don't, how much faster must you be going?


17. A golfer can give a golfball an initial speed of 40 m/s. The golfer can also vary the angle at which it leaves the tee. There is a 27-m wide pool of water 108 m away along the direction of the golfer's swing. What two angles can he hit the ball and have it land just in front of the pool? What two angles can he hit the ball and have it land just past the pool? What range of angles must be avoided to keep the golfball out of the water? Assume the balls don't roll after they hit the ground. The identity sin(2θ) = 2sin(θ)cos(θ) will be useful.


18. A stunt motorcyclist is trying to jump over fifteen buses set side to side. Each bus is 2.50 m wide and a 30.0° ramp has been installed on either side of the line of buses. What is the minimum speed at which she must travel to safely reach the other side? How long will she be in the air?


19. While preparing your cat's favourite meal, you drop the can and it rolls horizontally off the countertop and hits your cat on the head. Your cat's head is 0.95 m below the level of the countertop and 1.3 m away. Luckily, it was a can of Tender Vittles and the cat was not seriously hurt. What was the speed of the can as it left the countertop?

Questions? mike.coombes@kwantlen.ca