1 One dimensional kinematics for a single object Consider a free fall problem Consider up as the y direction A rock at the origin y 0 is released from rest at the top of a 100m tall building Draw a picture a Find the displacement vector b Find the speed of the rock at impact c Find the time interval of the fall to the ground 2 Beyond one dimension vectors in physics and relative motions Consider a relative motion problem Cleveland is 300 miles east of Chicago A plane leaves Chicago flying due east with a speed of 500 mph relative to the air a If there is no wind or the vel of air relative to ground is zero find the b The air is moving at 50 mph due south relative to the ground Where time t 0 to reach Chicago will be the plane be at the time t 0 3 Astronauts explore a newly discovered distant planet called W with an unknown gravitational acceleration constant gw Let up be the y direction and y 0 at the surface of the planet Hint draw a picture You do not need to know the mass of the rock a A rock is dropped with initial speed of zero from the surface into a 100 meters deep hole The final speed at impact is 1 m s find the average velocity vector b Find the displacement vector c Find the time interval of the drop d Find the gravitational acceleration vector e Find the value of gw 4 An object falls off a car traveling with speed of 20 m s in the x direction on flat ground The object was 0 3 m above the ground at that instant a How long does it takes to hit the ground b Find the y component of the velocity vector at impact c Find the x component of the velocity vector at impact d Find the speed of the object at impact e Find the magnitude of the displacement in the x direction while falling 5 A ball leave the ground at 37 degrees above the horizontal with a speed of 100 m s g 9 8 m s2 Hint draw a picture a How long does it takes to hit the ground b Find the y component of the velocity vector at impact c Find the x component of the velocity vector at impact d Find the speed of the object at impact e Find the magnitude of the displacement in the x direction at impact 6 A river has a constant width w in the x direction and the water is flowing with a speed of s in the y direction relative to the ground Draw a picture A swimmer starts at the origin 0 0 on one side of the river and swims across with a constant velocity vector of V x V y relative the water a How long does it take to swim across the river b Where will the swimmer be x y when the river has been crossed Later the swimmer wants to cross the river again and return to the origin with the same crossing time as before c Find the x component of the return velocity vector relative to the water d Find the y component of the return velocity vector relative to the water 7 At t 0 an ice hockey puck of mass moves on the ice with a constant velocity vector of 10 m s in the x direction There is a gravitational force in the y direction with Hint draw a free body diagram a The net force on the puck in the x direction at t 0 has a magnitude of b The net force on the puck in the y direction at t 0 has a magnitude of c The gravitational force vector on the puck is d Find the magnitude of the force on the puck due to the ice e Find the direction of the force on the puck due to the ice 8 Newton s law of motion Consider a contact force problem Consider 3 boxes on the x axis with box 1 in contact with box 2 and box 2 in contact with box 3 M 1 1kg M 2 2kg M 3 3kg The boxes are arranged from left to right in sequential order of 1 2 3 Draw a picture We denote the contact forces between each pair of boxes that are in contact as Fbon c is the force of b on c Now in addition an external force of F 10N x is applied to box 1 a If F2 on 3is the force of 2 on 3 What is the force of 3 on 2 b Find the magnitude of the net force vector acting on the three boxes c Which direction will the boxes move d Find the magnitude of the acceleration vector of box 3 e Find the magnitude of the vector F 2on 3