Since we're just getting started, I'll give you some hints as to how to go about tomorrow's problems. We went over problems 4 & 5 in class, so you should be OK with those I hope.
Problem 6: The main trick here is to keep track of the time in our equations very carefully. Object 1 starts moving T seconds earlier than object 2. If our clock starts at t=0 when object 2 starts moving, that means object 1 has been moving for T seconds already. Therefore, wherever we would normally write t in our equations for object 1, we should use (t+T) to account for the head start. With that in mind, since you're given the initial position and velocity for each you can just write down x(t) for each and find their difference.
Problem 7: Like the last problem, you know the starting position and velocity for each object, so write down the two x(t) equations. (a) The second ball is at rest when its velocity is zero. They'll collide when the two x(t) functions are equal. (b) Relative speed just means finding the velocity of each ball at the time of the collision and subtracting them.
Problem 8: You'll suspect it covers half the distance in half the time, but that's not quite right - the ball is steadily slowing down as it rises. Since it goes faster for the first half of the motion, it covers more distance. Write down x(t), and find out how long it takes to get to the top of the motion and what that maximum height is. Then evaluate x(t) at half that time and see how far it has gone.
Problem 6: The main trick here is to keep track of the time in our equations very carefully. Object 1 starts moving T seconds earlier than object 2. If our clock starts at t=0 when object 2 starts moving, that means object 1 has been moving for T seconds already. Therefore, wherever we would normally write t in our equations for object 1, we should use (t+T) to account for the head start. With that in mind, since you're given the initial position and velocity for each you can just write down x(t) for each and find their difference.
Problem 7: Like the last problem, you know the starting position and velocity for each object, so write down the two x(t) equations. (a) The second ball is at rest when its velocity is zero. They'll collide when the two x(t) functions are equal. (b) Relative speed just means finding the velocity of each ball at the time of the collision and subtracting them.
Problem 8: You'll suspect it covers half the distance in half the time, but that's not quite right - the ball is steadily slowing down as it rises. Since it goes faster for the first half of the motion, it covers more distance. Write down x(t), and find out how long it takes to get to the top of the motion and what that maximum height is. Then evaluate x(t) at half that time and see how far it has gone.
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