Two soccer players start from rest, 36 m apart. They run directly toward each ot

Question

Two soccer players start from rest, 36 m apart. They run directly toward each other, both players accelerating. The first player's acceleration has a magnitude of 0.59 m/s2. The second player's acceleration has a magnitude of 0.41 m/s2, (a) How much time passes before the players collide? (b) At the instant they collide, how far has the first player run? A dynamite blast at a quarry launches a rock straight upward, and 2.4 s later it is rising at a rate of 17 m/s. Assuming air resistance has no effect on the rock, calculate its speed (a) at launch and (b) 4.1 s after launch. Concept Simulation 2.3 offers a useful review of the concepts central to this problem. An astronaut on a distant planet wants to determine its acceleration due to gravity. The astronaut throws a rock straight up with a velocity of + 12.6 m/s and measures a time of 22.5 s before the rock returns to his hand. What is the acceleration (magnitude and direction) due to gravity on this planet? (positive = up, negative = down)

Explanation / Answer

1) a-) by relative velocity

36= (a1 + a2) t2/2

t=sqrt 36*2/(.59+.41)

=sqrt72

=8.48 sec

b) d1= a1 t2/2

.59*8.482/2= 21.24 m

2) 17=v-9.8t

v=17+9.8*2.4

v=40.52 m/s

b)v=40.52-4.1*9.8=0.34 m/s

3)net time in going one way t= 22.5/2 =11.25s

v=u-gt ,v=0

g=12.6/11.25

=1.12 m/s2

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