Question

When a cricket ball is thrown vertically upwards, it reaches a maximum height of 5 metres.
(a) What was the initial speed of the ball?
(b) How much time is taken by the ball to reach the highest point? $ \left( {{\text{g}} = 10\;{\text{m}}{{\text{s}}^{ - 2}}} \right) $ .

Answer 1

Hint :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. We use equations of motion to solve the question.
 $ {v^2} = {u^2} + 2as $
V= final velocity
U = Initial velocity
A= acceleration
S= displacement.

Complete Step By Step Answer:
Kinematics equations represent the fundamental idea of object motion, such as the location, velocity, and acceleration of an item at different intervals. The motion of an object in 1D, 2D, and 3D is governed by these three equations of motion. One of the most significant subjects in Physics is the derivation of the equations of motion. We'll teach you how to derive the first, second, and third equations of motion using the graphical, algebraic, and calculus methods in this article. In physics, equations of motion are equations that describe a physical system's behaviour in terms of its motion as a function of time. Components such as displacement(s), velocity (initial and final), time(t), and acceleration may be calculated using three equations of motion (a). The third motion equation is as follows: $ {v^2} = {u^2} + 2as $
Initial velocity, u=?
Since, Final velocity, v=0
Acceleration due to gravity, $ {\text{g}} = 10\;{\text{m}}{{\text{s}}^{ - 2}} $
Height be $ {\text{h}} = 5\;{\text{m}} $
Now upon Using relation, for a freely falling body we have
 $ {{\text{v}}^2} = {{\text{u}}^2} + 2{\text{gh}} $
 $ {(0)^2} = {({\text{u}})^2} + 2 \times ( - 10) \times 5 $
 $ 0 = {{\text{u}}^2} - 100 $
 $ {{\text{u}}^2} = 100 $
So, $ \Rightarrow {\text{u}} = 10\;{\text{m}}/{\text{s}} $
(b) Now upon Using relation $ v = u + gt $
 $ 0 = 10 + ( - 10)t $
-10=-10 t
 $ \Rightarrow {\text{t}} = 1{\text{sec}} $ .

Note :
Be careful while you mark the initial and final velocities. 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 in the SI (metric system).