Chapter - Kinematics | Part 3

 

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Chapter - Kinematics | Part 2

 

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A batter hits a base ball so that it leaves the bat with an initial speed $37\; m/s$ at an angle $53^{\circ}$. Find the position of the ball and the magnitude and direction of its velocity after $2$ seconds. Treat the baseball as a projectile.

Given,

$u = 37\;m/s$

$v = 53^{\circ}$

$t = 2\;sec$

$s = u_y*t - \frac{1}{2}\;g\;t^2$

$s = u\;Sin(\theta) * t - \frac{1}{2}\;g\;t^2$

$s = 37\;Sin (57) * 2 - \frac{1}{2}10 * 2^2$

⇒ $s = 39.5\;m$

And, Horizontal displacement = $u_y * t$

                                      $= u\; Cos\theta * 2 = 37 * Cos(53) * 2 = 44.52\;m$

∴ So, After 2 Sec the baseball will be lying $39.5\;m$ above its point of projection and $44.52\;m$ ahead of its point of projection.

Now, Let the vertical component of velocity will become $v_y$ after time 2 sec

$v_y = u_y -g*t = u\;Sin\theta - g\;t$

$v_y = 9.95 \;m/s$

$v_x = u_x = u\;Cos\theta = 22.27\;m/s$

Magnitude of velocity after $2\;s$ is,

$V = \sqrt{v_x^2 + v_y^2} = \sqrt{22.27^2 + 9.95^2} = 24.4\;m/s$

$\theta = tan^{-1}(\frac{v_y}{v_x}) = 24.06^{\circ}$ with the horizontal.

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A car travelling with a speed of $15\;m/s$ is braked and it slows down with uniform retardation. It covers a distance of $88 \; m$ as its velocity reduces to $7 \;m/s$. If the car continues to slow down with same rate, after what further distance will it be brought to rest?

Given,

$u = 15\;m/s$

$v = 7\;m/s$

$S = 88\;m$

$a = \;?$

$v^2 = u^2 + 2\;a\;s$

$7^2 = 15^2 + 2 * a * 88$

⇒ $a = -1 \;m/s^2$

∴ Retardation = $1\;m/s^2$

As car is going to stop;

$u = 7\;m/s$

$v = 0$

$a = -1\;m/s$

$s = \;?$

$v^2 = u^2 + 2\;a\;s$

$0 = 7^2 + 2 * (-1) * s$

$2s = 49$

⇒ $s = 24.5\;m$

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E1.3 Kinematics (Projectile Motion):

In topic Kinematics, previously we almost talk about one dimensional motion. Now from this session, let's start to talk about two dimensional motion - called Projectile motion. In such type of motion, gravity is the only factor acting on our objects (neglecting the air resistance, acceleration due to gravity is downward and constant).

Any object thrown into atmosphere so that it falls under the effect of gravity alone is called Projectile motion.

Projectile motion: is a form of motion in which an object (particle) i.e. called a projectile is thrown near the Earth's surface, and it moves along a curved path under the action of gravity only. (wikipedia)

We have different types of Projectile such as: 

I) Stone thrown horizontally
II) A bomb dropped from an airplane
III) Any object dropped from the windows of a Moving train.

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