Kinematics: The Geometry of Motion Exercise 3 Solutions | Basic Mathematics Grade XI by Sukunda Pustak Bhawan


In this page, you can find the complete solutions of the third exercise of Kinematics: The Geometry of Motion chapter from Basic Mathematics Grade XI book published and distributed by Sukunda Pustak Bhawan.

In the above-mentioned book, Kinematics is the 22nd chapter and has three exercises only. Out of which, this is the solution of the third exercise.


Check: Basic Mathematics Grade 11 (Sukunda Publication) Guide:

Grade 11 Basic Mathematics by Sukunda Pustak Vawan Notes and Solutions | Nepal


Disclaimer:

Answers mentioned here are not solved by teachers. These are the solutions written by a student of Grade 11. Answers are all correct. However, the language or process of solving the questions might be informal and in examinations, you might have to add little more language and show more calculations than what has been done here. So, we highly encourage you to view these solutions as guide rather than just copying everything mentioned here.


Here, we have used the following notations:

u = intial velocity

a = acceleration

v = final velocity

t = time



1 i) A particle slides down a smooth plane inclined at an angle of 30 to the horizon. Find the velocity of the particle at the end of 4 s. (g = 10m/s^2)

Solution:

Here,

$g = 10 m/s^2$

$\theta = 30^o$

$t = 4s$

$u = 0 m/s$

We know,

$v = u + (g sin\theta)t$

$or, v = 0 + (10 sin 30) * 4$

$or, v = 10 * 1/2 * 4$

$\therefore v = 20 m/s$


1 ii) A ball is projected up a smooth plane with velocity 25 m/s. If the inclination of the plane to the horizon be 30, find the velocity of the ball when it travels a distance of 22.5 m. (g = 10 m/s^2).

Solution:

Here,

$u = 25 m/s$

$\theta = 30^o$

$h = 22.5 m$

$g = - 10 m/s^2$ [ Acting downwards but u is acting upwards ]

We have,

$v^2 = u^2 + 2 (gsin\theta)h$

$or, v^2 = 25^2 + 2 ( -10 * sin 30) * 22.5$

$or, v^2 = 625 - 225$

$or, v^2 = 400$

$\therefore v = 20 m/s$ [velocity is acting upwards ]


6. A ball rolling down a smooth slope passes posts on the slope at equal distances. The velocities when passing three successive posts are x,y,z. Prove that $x^2, y^2, z^2$ are in A.P.

9. Show that the time of fall down an inclined plane of a given base is least when the inclination is $45^o$.

Solution:




About the Textbook:

Name: Basic Mathematics Grade XI
Author(s): D.R. Bajracharya | R.M. Shresththa | M.B. Singh | Y.R. Sthapit | B.C. Bajracharya
Publisher: Sukunda Pustak Bhawan (Bhotahity, Kathmandu)
Telephone: 5320379, 5353537
Price: 695 /- (2078 BS)