Answer:
(a) a = 2.44 m/s²
(b) s = 63.24 m
Explanation:
(a)
We will use the second equation of motion here:
where,
s = distance covered = 47 m
vi = initial speed = 0 m/s
t = time taken = 6.2 s
a = acceleration = ?
Therefore,
<u>a = 2.44 m/s²</u>
<u></u>
(b)
Now, we will again use the second equation of motion for the complete length of the inclined plane:
where,
s = distance covered = ?
vi = initial speed = 0 m/s
t = time taken = 7.2 s
a = acceleration = 2.44 m/s²
Therefore,
<u>s = 63.24 m</u>
(a)
For an object in free-fall, the vertical position at time t is given by:
where
h is the initial vertical position
u is the initial vertical velocity
g = 9.8 m/s^2 is the acceleration of gravity
t is the time
In this problem,
h = 250 m
u = 0 (the stone starts from rest)
So, the vertical position of the stone is given by
(b) 7.14 s
The time it takes for the stone to reach the ground is the time t at which the vertical position of the stone becomes zero:
y(t) = 0
Which means
So for the stone in the problem, we have
Solving for t, we find:
(c) -70.0 m/s (downward)
The velocity of an object in free fall is given by the equation
where
u is the initial velocity
g = 9.8 m/s^2 is the acceleration of gravity
t is the time
Here we have
u = 0
So if we substitute t = 7.14 s, we find the velocity of the stone at the time it reaches the ground:
The negative sign means the direction of the velocity is downward.
(d) 6.94 s
In this situation, the stone is thrown downward with an initial speed of 2 m/s, so its initial velocity is
u = -2 m/s
So the equation of the vertical position of the stone in this case is
By solving the equation, we find the time t at which the stone reaches the ground.
We find two solutions:
t = -7.35 s
t = 6.94 s
The first solution is negative, so it has no physical meaning, therefore we discard it. So, the time it takes for the stone to reach the ground is:
t = 6.94 s