17.5kg Olivia is running to Elizabeth who is standing still with a velocity of 8 ms and jumps into her arms to be held if Elizab
1 answer:
The final velocity is 1.64 m/s
Explanation:
We can solve this problem by using the law of conservation of momentum: in fact, in absence of external forces, the total momentum of the two girls must be conserved before and after the collision.
Therefore we can write:
where:
is the mass of Olivia
is the initial velocity of Olivia
is the mass of Elizabeth
is the initial velocity of Elizabeth
is the final combined velocity of the two girls
Re-arranging the equation and substituting the values, we find the final velocity:
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a.
Let's call:
the time calculated from the moment Diane starts her motion and
the time calculated from the moment Derek starts his motion. Derek starts his motion 4 seconds before Diane: this means that has an "advantage" of 4 seconds, so we can write
Then:
is the uniform speed of Derek
Derek is moving in a uniform motion, so Derek's position will be given by (assuming that the starting position is zero):
We see that this is correct: in fact, when t=0 (instant when Diane starts her motion), Derek has already travelled for
b.
t is the time calculated from the moment Diane starts her motion. Diane is moving by accelerated motion, with constant acceleration and initial velocity
, so its position at time t is given by the law of uniform accelerated motion:
c. t = 8.74 s
The time t at which Diane catches up with Derek is the time t at which the positions of the two persons is equal:
By solving, we have:
Which has two solutions:
t = -2.74 s --> negative, we can discarde it
t = 8.74 s --> this is our solution
d. 76.4 m
When Diane catches Derek, at t=8.74 s, she has covered the following distance:
We can verify that Derek is at the same position: