Their velocity afterwards is 2.88 m/s east
Explanation:
We can solve this problem by using the law of conservation of momentum. In fact, for an isolated system (= no external force), the total momentum must be conserved before and after the collision. So we can write:
where: in this case:
is the mass of the first player
is the initial velocity of the first player (choosing east as positive direction)
is the mass of the second player
is the initial velocity of the second player
is their combined velocity afterwards
Solving for v, we find:
And the sign is positive, so the direction is east.
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This is a conservation of momentum problem! Here's how to do it:
The height at time t is given by
h(t) = -4.91t² + 34.3t + 1
When the ball reaches maximum height, its derivative, h'(t) = 0.
That is,
-2(4.91)t+34.3 = 0
-9.82t + 34.3 = 0
t = 3.4929 s
Note that h''(t) = -9.82 (negative) which confirms that h will be maximum.
The maximum height is
hmax = -4.91(3.4929)² + 34.3(3.4929) + 1
= 60.903 m
Answer:
The ball attains maximum height in 3.5 s (nearest tenth).
The ball attains a maximum height of 60.9 m (nearest tenth)
The AU ... Astronomical Unit ... used to be defined as the average distance between the Sun and Earth during the year.
Now it's defined as 149,597,870,700 meters exactly.
