Mary wants to throw a can straight up into the air and then hit it with a second can. She wants the collision to occur at height h=10.0 m above the throw point. In addition, she knows that she needs t1=4.0 s between successive throws. Assuming that she throws both cans with the same speed. Take g to be 9.81 m/s2.
hint: you might want to look at Professor's Lewin's Help Session before you attempt this problem.
(a) How long it takes (in s) after the first can has been thrown into the air for the two cans to collide?
Δt=
unanswered
(b) Find the initial speed of the cans (in m/s).
v0=
22secs
16.3 m/s
To solve this problem, we need to break it down into two parts.
(a) How long it takes (in s) after the first can has been thrown into the air for the two cans to collide?
To find the time it takes for the two cans to collide, we need to consider the vertical motion of the two cans. We can use the kinematic equation of motion:
y = y0 + v0t - (1/2)gt^2,
where y is the vertical position, y0 is the initial vertical position, v0 is the initial velocity, t is the time, and g is the acceleration due to gravity.
For the first can, we have:
y1 = 0 + (1/2)gt^2,
For the second can, we have:
y2 = h - (1/2)g(t - t1)^2,
where h is the height at which the collision occurs and t1 is the time between successive throws.
To find the time it takes for the two cans to collide, we set y1 equal to y2 and solve for t:
(1/2)gt^2 = h - (1/2)g(t - t1)^2.
Now, let's substitute the given values:
h = 10.0 m,
t1 = 4.0 s, and
g = 9.81 m/s^2.
Plugging in these values, we get the following equation:
(1/2)(9.81)t^2 = 10 - (1/2)(9.81)(t - 4)^2.
Now, we can solve this equation for t to find the time it takes for the two cans to collide.
(b) Find the initial speed of the cans (in m/s).
Once we have found the time it takes for the cans to collide, we can use that time to find the initial speed of the cans.
The initial speed can be found using the equation:
v0 = (y - y0 - (1/2)gt^2) / t,
where y is the final vertical position, y0 is the initial vertical position, g is the acceleration due to gravity, and t is the time it takes for the cans to collide.
Substituting the given values, we can find the initial speed of the cans.