A shell is shot with an initial velocity of 20 m/s, at an angle of theta0 = 60 d
ID: 2070516 • Letter: A
Question
A shell is shot with an initial velocity of 20 m/s, at an angle of theta0 = 60 degree with the horizontal. At the top of the trajectory, the shell explodes into two fragments of equal mass (Fig. 9-46). One fragment, whose speed immediately after the explosion is zero, falls vertically. How far from the gun does the other fragment land, assuming that the terrain is level and that air drag is negligible? ssm FIG. 9-46 Problem 15. Ricardo, of mass 80 kg, and Carmelita, who is lighter, arc enjoying Lake Merced at dusk in a 30 kg canoe. When the canoe is at rest in the placid water, they exchange seats, which are 3.0 m apart and symmetrically located with respect to the canoe's center. If the canoe moves 40 cm i horizontally relative to a pier post, what is Carmelita's mass?Explanation / Answer
Problem 15:
max height of shell = v^2 / 2g = (20sin60)^2 / 2*9.8 = 15.306 m
horiz speed at max height = v cos@ = 20*cos60 = 10
after explosion, speed of moving pieces doubles by cons of momentum, to 20
time to fall = time to rise to max height = vsin@/g = 20*sin60/9.8 = 1.7674 seconds
total horiz distance = 10 * 1.7674 + 20 * 1.7674 = 53.02 m
Problem 16: center of mass of canoe stays in the same place. Initially,
Carm is at x = 0 center of canoe is at x = 150 Richard is at 300
write cm equation: position of cm = (1/total mass) (M * 0 + 150*30 + 300*80)
= (1/total mass) * 28500
after they move, Richard is at 40 center of canoe is at 190 Carm is at 340
again, write cm equation: position of cm = (1/total mass) (40*80 + 190*30 + M*340 )
= (1/total mass) (8900 + 340M)
set equations equal to each other:
28500 = 8900 + 340 M
19600 = 340 M
M = 57.6 kg is Carm's mass
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