To solve this problem we will apply the concepts related to Newton's second law that relates force as the product between acceleration and mass. From there, we will get the acceleration. Finally, through the cinematic equations of motion we will find the time required by the object.
If the Force (F) is 42N on an object of mass (m) of 83000kg we have that the acceleration would be by Newton's second law.

Replacing,


The total speed change
we have that the value is 0.71m/s
If we know that acceleration is the change of speed in a fraction of time,

We have that,


Therefore the Rocket should be fired around to 1403.16s
As per FBD while its accelerating upwards
we can say that

here normal force is given as


now mass is given as


now we will have


Now while accelerating downwards we can say by FBD

again plug in all values


<u>Answer:</u>
a) Height of cliff = 44.145 meter
b) 7.5 meter far from its base the diver hit the water.
<u>Explanation:</u>
We have equation of motion ,
, s is the displacement, u is the initial velocity, a is the acceleration and t is the time.
Diver's vertical motion:
Initial velocity = 0 m/s, acceleration = 9.8
, we need to calculate displacement when time is 3 seconds.

So height of cliff = 44.145 meter.
b) Diver's horizontal motion:
Initial velocity = 2.5 m/s, acceleration = 0
, we need to calculate displacement when time is 3 seconds.

So 7.5 meter far from its base the diver hit the water.