coordinate system in which up is positive and down is negative.

Math: To show your understanding of kinematics, using the quadratic formula is off-limits for this Exam.

In this assignment, Fastball, a teenager who became a superhero after catching a radioactive baseball, can now fly, and she can throw any object at jet aircraft speeds, with no air resistance at all.

1. Floating at rest high above the ground, Fastball (FB) decides to toss a donut to her pet, Supersparrow (SS), circling several kilometers above her. In the next question, you'll make a choice and then calculate the minimum velocity the donut needs in order to reach SS. For now, though, explain why you can't set the donut's initial velocity vi to 0 m/s in that question. Illustrate with a sketch. 1-2 complete sentences, no more.

2. SS is 7 km above Fastball (her altitude is irrelevant don't bother about it), then calculate the minimum launch velocity FB must give the donut in order for it to rise to SS's altitude. Be careful with units! Check: does your minimum velocity give the correct displacement?

3. Calculate how much time it'll take the donut to reach SS's altitude when launched at the velocity just found. Check: does your time give the correct displacement?

4. Unfortunately, Supersparrow is going to reach the point directly above Fastball 14.7 s sooner than the time found in Q3, so the donut has to be thrown faster to get to SS on time. Ex: if you'd found the donut would take 100 s to reach SS's altitude, it needs to get there in just 80-90 s, instead. State the new time, then calculate the new minimum launch velocity needed to make the donut reach SS on time. Tip: the donut won't stop when it reaches SS's altitude if thrown faster than before. Checks: should be faster than the velocity in Q2! Does the donut rise the correct distance in the required time?

5. Fastball launches the donut at the velocity found in Q4, and although it reaches SS on time, SS just lets it pass. It rises to some unknown maximum height, and then begins falling back down again. Realizing he's hungry after all, SS swoops around, catching the donut when it's 3.20 km above Fastball. How many km above or below Fastball does SS catch the donut?

6. Make a sketch showing the donut's entire flight (launch to interception), with four labeled vectors showing the donut's initial and final velocities (vi, vf,), displacement (y) and acceleration (a). The sketch should be at least as large as your hand, so that all parts of it are easy to read online.

7. What is the donut's displacement y in km, from launch to interception, including its sign? Explain why you can answer this question without knowing the donut's maximum height or making any calculations at all.

8. Shortly, you're going to calculate the donut's velocity at the instant (before) SS catches it. But first, is the donut's velocity positive or negative at that instant? Explain the physics; no math.

9. And should the donut's velocity at that instant be faster or slower than the launch velocity found in Q4? Explain without math.

10. Treating the entire flight of the donut, from launch (at the initial velocity found in Q4) to interception, as a single unbroken interval of motion, calculate the donut's velocity the instant (before) SS catches it. This means not breaking the flight into several pieces and solving them separately. Check against your predictions in Q8-9.

11. Calculate the donut's total flight time from launch to interception, again not breaking the flight into several pieces and solving them separately. Check: should the time be more or less than the time calculated in Q3?

Date : Velocity is then there is no 1> if initial velocity zerce acceleration on upside to g' is acting downwards move higher instead AVEO tg m/s ? & for minimum velocity let the donut just touch SS. So at the point of touch ita velocity becomes zero Ser from recated v = U - 2as 0 = (l/min)2 - 2x9.81x7000 Umin = 370.6 m/s 32 from, v=u-at 0=370.6 -9.816 t-37.38 sec