Answer:
a. Vf = 39.24 [m/s]
b. Vf = 31.24 [m/s]
c. Vf = 47.24 [m/s].
Explanation:
To solve this problem we can use the following equation of kinematics. We have to keep in mind that the gravitational acceleration acts downwards, therefore when the rock falls towards the abyss it has the same direction of the acceleration and that is why the gravitational acceleration has a positive sign in the equation.

where:
Vf = final velocity [m/s]
Vo = initial velocity = 0 (when the rock is dropped)
g = gravitational acceleration = 9.81 [m/s²]
t = time = 4 [s]
a.
![v_{f}=0+9.81*4\\v_{f}= 39.24 [m/s]](https://tex.z-dn.net/?f=v_%7Bf%7D%3D0%2B9.81%2A4%5C%5Cv_%7Bf%7D%3D%2039.24%20%5Bm%2Fs%5D)
b.
In this particular situation, the acceleration will be taken as negative because the gravity is pointing in the opposite direction of the movement of the rock.
![v_{f}=8-(9.81*4)\\v_{f}=-31.24[m/s]](https://tex.z-dn.net/?f=v_%7Bf%7D%3D8-%289.81%2A4%29%5C%5Cv_%7Bf%7D%3D-31.24%5Bm%2Fs%5D)
The negative sign in the answer tells us that the rock no longer moves up instead it does downwards when 4 seconds have passed.
c.
![v_{f}=8+(9.81*4)\\v_{f}=47.24[m/s]](https://tex.z-dn.net/?f=v_%7Bf%7D%3D8%2B%289.81%2A4%29%5C%5Cv_%7Bf%7D%3D47.24%5Bm%2Fs%5D)
Answer:
time taken with speed 23 km/h will be 1.8 hours or 1 hour 48 minutes
Explanation:
Given:
Time is inversely proportional to the speed
mathematically,
t ∝ (1/r)
let the proportionality constant be 'k'
thus,
t = k/r
therefore, for case 1
time = 3 hr
speed = 14 km/hr
3 = k/14
also,
for case 2
let the time be = t
r = 23 km/h
thus,
we have
t = k/23
on dividing equation 2 by 1
we get

or

or
t = 1.8 hr = or 1 hour 48 minutes ( 0.8 hours × 60 minutes/hour = 48 minutes)
Answer:
v = 8.96 m/s
Explanation:
Initial speed of the ball, u = 10 m/s
It caught 1 meter above its initial position.
Acceleration due to gravity, 
We need to find the final speed of the ball when it is caught. Let is equal to v. To find the value of v, use third equation of motion as :



v = 8.96 m/s
So, the speed of the ball when it is caught is 8.96 m/s. Hence, this is the required solution.