Physics Challenge Question 1: Precision and Accuracy
Physics Challenge Question 14: Mid-air explosion
Due in class Friday 1/30/2009
A cannon shoots a grenade into the air. The grenade is shown on the figure to the right. The grenade has a mass of 50 kg and travels to the right with a speed of 100 m/s.
Part 1 (1 point)
What is the initial momentum of the grenade (magnitude and direction)?
Part 2 (2 points)
The grenade explodes in mid-air and breaks into three pieces, as shown on the figure. You manage to measure the mass of all fragments, but only the velocity of two of them.
Use momentum conservation to find the velocity (both direction and the magnitude) of the third fragment. (Be careful with the directions of the velocities!) (Hint: The three pieces originally “stick together.”)
Part 3 (2 points) (challenging!)
You now shoot off a new grenade, with identical mass and velocity to the one in part 1. Again, it explodes in mid-air. This time, however, it forms just two fragments. One flies straight up, and one downward and to the right, as shown on the figure.
Use momentum conservation to find the speed (just the magnitude) of the second fragment. (Hints: Our momentum conservation equation can be applied separately to both the vertical and horizontal directions. Use it twice, once for each direction, and find both the horizontal and vertical component of v. Then, use the Pythagorean theorem to find the magnitude of v.)
-----------------------
v = ?
25 kg
25 kg
15 kg
10 m/s
v = ?
30 m/s
15 kg
20 kg
20 m/s
v = 100 m/s
m = 50 kg
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