Question

A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate
(1) The maximum height to which it rises.
(2) The total time it takes to return to the surface of the earth.

Answer 1

The rate of change of an object's location with regard to a frame of reference is its velocity, which is a function of time. A definition of an object's speed and direction of travel (e.g. 60 km/h to the north) is identical to velocity. In kinematics, the branch of classical mechanics that explains the motion of bodies, velocity is a basic notion. We use equations of motion to solve the problem.

Formula Used:
$2gs{\text{ }} = {\text{ }}{v^2}\;-{\text{ }}{u^2}$
G = acceleration due to gravity
V = final velocity
U = initial velocity
S = displacement

Complete answer:
Velocity is a physical vector quantity that requires both magnitude and direction to define. Speed is the scalar absolute value (magnitude) of velocity, and it is a coherent derived unit whose quantity is measured in metres per second (m/s) in the SI (metric system).
The ball's initial velocity (u) is 49 metres per second.
The ball's greatest height velocity (v) Equals 0.
g = $9.8m{s^{ - 2}}$
Let us consider the time is t to reach the maximum height H.
Consider a formula,
$2gs{\text{ }} = {\text{ }}{v^2}\;-{\text{ }}{u^2}$
Hence upon substituting
$2{\text{ }} \times {\text{ }}\left( { - {\text{ }}9.8} \right){\text{ }} \times {\text{ }}H{\text{ }} = {\text{ }}0{\text{ }}-{\text{ }}{\left( {49} \right)^2}$
so
– 19.6 H = – 2401
We get
$\Rightarrow$H = 122.5 m
Now consider a formula,
v = u + g × t
here
0 = 49 + (- 9.8) × t
hence
–49 = – 9.8t
therefore
$\Rightarrow$t = 5 sec

Note: Never forget to memorise the formulae of equations of motion. Equations of motion are physics equations that describe a physical system's behaviour in terms of its motion as a function of time. The equations of motion, more particularly, explain the behaviour of a physical system as a collection of mathematical functions expressed in terms of dynamic variables. Typically, these variables are geographical coordinates and time, but they may also incorporate momentum components.