Updated 1/18/19

This year we are appoaching kinematics (describing the motion of an object) starting Newton's Laws. This means we will know the acceleration and some boundary conditions. Integration and application of those boundary conditions will complete the description.

Be sure to clearly show your mathematical work, in a well organized way, for any numerical values you determine in the course of addressing these problems.

1) Depending on how this course has been structured we may have talked about sailing in space using sunlight to provide propulsion. Such systems have actually been tested and a plausible acceleration for a space sailer is 2 mm/s/s. In very rough terms the Apollo space craft travels to the moon at constant speed. Given that the moon is a distance of 4^.10⁵ km away from the earth and the average speed of the Apollo capsule is constant at 6.7^.10³ km/h which spacecraft gets to the moon first and by how much? How fast is each one going when it passes the moon? What assumptions have you made baout this problem to make it tractable? Which would get to Mars first (a linear distance of 8 ^.10⁷km)?

[Apollo by about 10 days, space sail is 5x faster to Mars]

2) A stationary car is initially some distance behind a stopped truck. Both begin to accelerate simultaneously. The car accelerates at 1.8 m/s/s and the truck at 1.2 m/s/s. The car passes the truck when the truck has traveled 48 m. How long did it take the car to catch up to the truck? How far behind the truck did the car start?

[9 s, 24 m]

3) Let's apply these ideas to a real life situation. Imagine the traffic on the parkway is moving along at a steady speed of 20 m/s (a little over 45 mph). Your car can accelerate from 0 to 30 m/s in 11 s. Assume it takes 3 sec after the lead car passes to pull out into traffic where your initial speed is 5.0 m/s.What would be meaningful to figure out here - how far apart do the cars have to be for this to be safe for you? Start by figuring out whatever you can and see if you can build a pathway to an answer. Focus on process and answers will come.

[2.7 (m/s)/s, 8.5 s, 102 m]

4) You are at a supermarket in Seattle and the parking lot is quite sloped. As you get out of your car you notice a shopping cart escape from a dad trying to manage kids and the cart simultaneously. The cart is 20 downhill from you and has an acceleration of 0.5 (m/s)/s. You spring into action with an acceleration of 2.0 m/s/s with a maximum speed of 8 m/s. How does our tale end? Do you catch the cart? Where and when? What happens then?

[5.4 s and 7.2 m from dad]

5) A woman in an apartment sees a flower pot fall past her window. She observes that it takes 180 ms for the pot to traverse her 2.3 m tall window. Where did the pot start falling from (at v=0!)? Undoubtedly the woman will report the resident of the appropriate apartment to the building super for poor cleaning habits. This is a problem which benefits from observing all the steps in the problem solving framework.

[1.2 s, 7.2 m up]

 

6) (Calc) The NASA shuttle has a weight of 93^.10⁶ N and generates a constant thrust (force) of 90^.10⁶ N during the firing of its main engines and solid rocket boosters. While the engines are firing fuel is being consumed at an alarming rate which reduces the mass at a rate of 5.7^.10⁴ kg/s. When will the shuttle actually begin to lift off the ground? What is the velocity of the shuttle 40 s (assuming all these numbers are valid) after the shuttle begins to rise?