Explanation:
Given that,
Mass of the cart,
Mass of the cart 2,
Final speed of cart 2,
Final speed of cart 1 is 0 as it comes to rest.
Let us assume that the initial velocity of the cart 2 is 0. So using the conservation of linear momentum as :
So, the initial velocity of the 1.0-kg cart is 0.9 m/s.
A) 2.02 s
To find the time it takes for the bunny to reach the rocks below the cliff, we just need to analyze its vertical motion. This motion is a free fall motion, which is a uniformly accelerated motion. So we can use the suvat equation:
where
s is the vertical displacement
u is the initial vertical velocity
a is the acceleration
t is the time
For the bunny here, choosing downward as positive direction,
(initial vertical velocity is zero)
s = 20 m
(acceleration of gravity)
And solving for t, we find the time of flight:
B) 14.1 m
For this part, we need to consider the horizontal motion of the bunny.
The horizontal motion of the bunny is a uniform motion with constant velocity, which is the initial velocity of the bunny:
Therefore the distance covered after time t is given by
And substituting the time at which the bunny hits the ground,
t = 2.02 s
We find how far the bunny went from the cliff:
C) 21.0 m/s at below the horizontal
The horizontal component of the velocity is constant during the entire motion, so it will still be the same when the bunny hits the ground:
Instead, the vertical velocity is given by
And substituting t = 2.02 s, we find the vertical velocity at the moment of impact:
So, the magnitude of the final velocity is
And the angle is given by
below the horizontal