Question

A ball is thrown up with a speed of 40 m/s. The
time taken to reach the maximum height by the
ball is _ sec. (take the value of g = 10 m/s2)​

Answer 1

Given :

A ball is thrown up with a speed of 40 m/s. g = 10 m/s²

To find :

The time taken to reach the maximum height by the  ball is _ sec.

Solution :

Initial velocity of ball (u) = 40 m/s

At maximum height , v = 0 m/s

Gravitational acceleration, g = -10 m/s²  (As it is thrown upwards)

Now using 1st equation of motion,

v = u + gt

⇒ 0 = 40 -10t

⇒ - 40 = - 10t

⇒ t = -40/-10

⇒ t = 4 s

Therefore,

Time taken to reach maximum height =  4s

Equations of motion :

* v = u + at

* s = ut + 1/2 at²

* v² - u² = 2as

Answer 2

Answer :-

$\: \: \boxed{\boxed{\rm{\mapsto \: \: \: Firstly \: let's \: understand \: the \: concept \: used}}}$

Here the concept of Equations of Motions have been used. According to this, if we know the equations of motion, then we can easily find out Displacement (s), Final Velocity (v), Time (t), Acceleration (a) and Initial Velocity (u).

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★ Formula Used :-

$\: \: \large{\boxed{\boxed{\bf{\leadsto \: \: v \: - \: u \: = \: a \: \times \: t}}}}$

★ Question :-

A ball is thrown up with a speed of 40 m/s. The time taken to reach the maximum height by the ball is _ sec. (take the value of g = 10 m/s2)

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★ Solution :-

Given,

» Initial Velocity of the Ball = u = 40 m/sec

» Final Velocity of the Ball = v = 0 m/sec

(since the vall goes up and looses all its kinetic energy and thus velocity turns to be 0)

» Acceleration due to gravity = a

= -10 m/sec²

(since the ball is going in opposite direction to gravity)

Using the First Equation of Motion, we get,

✒ v - u = a × t

✒ 0 - 40 = (-10) × t

✒ -40 = -10 × t

$\: \: \Longrightarrow \: \: \bf{t \: = \: \dfrac{\not{-} 40}{\not{-} 10}}$

$\: \large{\boxed{\bf{t \: = \: 4 \: sec}}}$

• Hence, the time taken by the ball to reach the highest point = t = 4 sec.

$\: \: \\ \boxed{\rm{\leadsto \: \: Thus, \: time \: taken \: by \: the \: ball \: is \: \underline{\boxed{\boxed{\bf{4 \: sec}}}}}}$

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$\: \: \: \huge{\boxed{\tt{\large{More \: to \: know \: :-}}}}$

• Newton's First Law of Motion : It states that every body continues in its state of rest or of uniform motion along a straight line, unless an external force is applied to change that state. This law defines force.

• Newton's Second Law of Motion : It states that the rate of change of momentum of a body is directly proportional to the applied force and the change in momentum takes place in the direction of force applied. This law gives a measure of the force.

• Newton's Third Law of Motion : It states that to every action, there is an equal and opposite reaction.

• Second Equation of Motion :-

s = ut + ½ (at²)

• Third Equation of Motion :-

v² - u² = 2as