A man drops a rock into a well. (a) the man hears the sound of the splash 2.90 s after he releases the rock from rest. the speed
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To develop the problem, we require the values concerning the conservation of momentum, specifically as given for collisions.
By definition the conservation of momentum tells us that,
To find the speed at which the arrow impacts the apple we turn to the equation of time, in which,
The linear velocity of an object is given by
Replacing the equation of time we have to,
Velocity two is neglected since there is no velocity of said target before the collision, thus,
Clearing for m_2
Acceleration is given by:
where
v is the final velocity
u is the initial velocity
t is the time interval
Let's apply the formula to the different parts of the problem:
A)
Let's convert the quantities into SI units first:
t = 4.0 min = 240 s
So the acceleration is
B)
As before, let's convert the quantities into SI units first:
t = 94 s
So the acceleration is
C)
For this part we have to use a different formula:
where we have
v = 0 is the final velocity
u = 89.2 m/s is the initial velocity
a is the acceleration
d = 75 m is the distance covered
Solving for a, we find