Recent questions tagged ch4

It is possible to project a particle with a given velocity in two possible ways so as to make it pass through a point at a horizontal distance R from the point of projection .If $H_1$ and $H_2$ are the corresponding maximum height and $H$ is maximum height when the particle is projected at $45^{\circ}$ with the same speed, then what is $H_1+H_2$

asked Jul 15, 2014 by meena.p

1 answer

It is possible to project a particle with a given velocity in two possible ways so as to make it pass through a point at a horizontal distance R from the point of projection . If $t_1$ and $t_2$ are the time taken to reach this point in two possible ways then what is $t_1t_2$?

asked Jul 15, 2014 by meena.p

1 answer

A ball rolls off the top of a stairway with a velocity u. If the height of each step is h, the breadth is b and the ball hits the edge of nth steps, the find the value of n.

asked Jul 15, 2014 by meena.p

1 answer

A man can throw a stone 60 m away . How high can he throw the stone vertically upward?

asked Jul 15, 2014 by meena.p

1 answer

A car travels east at a speed of $30m/s^{-1}$ . It turns left through an angle of $90^{\circ}$ and continues to travel with the same speed. What is the change in its velocity ?

asked Jul 15, 2014 by meena.p

1 answer

A body is projected with speed $v_1$ at an angle of $45^{\circ}$ to the horizontal from a point A. At the same instant, another body is projected vertically below the highest point of the path of the first body, Both the bodies will collide if $v_1/v_2$ is

asked Jul 14, 2014 by meena.p

1 answer

A projectile is thrown with velocity u making angle $\theta$ with vertical. It just crosses the tops of two poles each of height h after 1 second respectively. The maximum height of projectile is

asked Jul 14, 2014 by meena.p

1 answer

From a point on the group at a distance 2 meters from the foot of a vertical wall , a ball is thrown at an angle $45^{\circ}$ which just clear the top of the wall and afterwards strikes the ground at a distance 4 m on the other side. The height of the wall is

asked Jul 14, 2014 by meena.p

1 answer

The velocity at the maximum height of a projectile is half of its initial velocity of projection u. Its range on horizontal plane is

asked Jul 14, 2014 by meena.p

1 answer

A body is projected at an angle $30^{\circ}$ to the horizontal with a speed $39.2 ms^{-1}$.What is the angle of projectile with the horizontal after 2 seconds ? (take $g= 9.8\;ms^{-2} )$

asked Jul 14, 2014 by meena.p

1 answer

The velocity of projection of an oblique projectile is $(6i +8j)m/s$ . The horizontal range of projectile is $( g=10 m/s)^2$

asked Jul 14, 2014 by meena.p

1 answer

The range of projectile which is launch at an angle of $15^{\circ}$ with the horizontal is $1.5 \;km$ what is the range of the projectile if it is projected at an angle of $45^{\circ}$ to the horizontal ?

asked Jul 14, 2014 by meena.p

1 answer

Two bodies are projected from the same point with the same speed but in different directions so as to have the same range. The ratio of their times of flight are .

asked Jul 11, 2014 by meena.p

1 answer

The greatest distance to which a man throw a stone is a. The greatest height to which he can throw it will be

asked Jul 11, 2014 by meena.p

1 answer

An object is thrown along a direction inclined at an angle of $45^{\circ}$ with the horizontal range of the particle is equal to

asked Jul 11, 2014 by meena.p

1 answer

State whether the following statement is true or false. Justify. Let $P(n)$ be a statement and let $P(k) \Rightarrow P(k+1)$, for some natural number $k$, then $P(n)$ is true for all $n \in N$.

asked May 6, 2014 by thanvigandhi_1

0 answers

If $P(n) : 2n < n!, n \in N$, then $P(n)$ is true for all $n \geq $______ .

asked May 6, 2014 by thanvigandhi_1

1 answer

Choose the correct answer if $x^n-1 $ is divisible by $ x - k$, then the least positive integral value of $k$ is

asked May 6, 2014 by thanvigandhi_1

0 answers

Choose the correct answer for all $n \in N, 3.5^{2n+1}+2^{3n+1}$ is divisible by

asked May 6, 2014 by thanvigandhi_1

1 answer

Choose the correct answer if $10^n+3.4^{n+2}+k$ is divisible by 9 for all $n \in N$, then the least positive integral value of $k$ is

asked May 6, 2014 by thanvigandhi_1

0 answers

Prove that number of subsets of a set containing $n$ distinct elements is $2^n$, for all $ n \in N$ by using principle of mathematical induction.

asked May 6, 2014 by thanvigandhi_1

0 answers

Prove that, $ \large\frac{1}{n+1}$$+ \large\frac{1}{n+2}$$+...+\large\frac{1}{2n}$$ > \large\frac{13}{24}$, for all natural numbers $n > 1$ by using principle of mathematical induction.

asked May 6, 2014 by thanvigandhi_1

0 answers

Show that $ \large\frac{n^5}{5}$$+\large\frac{n^3}{3}$$+\large\frac{7n}{15}$ is a natural number for all $n \in N$ by using the principle of mathematical induction.

asked May 6, 2014 by thanvigandhi_1

0 answers

Prove that, $ \sin \theta + \sin 2\theta + \sin 3\theta+...+ \sin n\theta = \large\frac{\Large\frac{\sin n \theta}{2} \sin \Large\frac{(n+1)}{2} \theta}{\sin \Large\frac{\theta}{2}}$, for all $ n \in N$ by using principle of mathematical induction.

asked May 6, 2014 by thanvigandhi_1

0 answers

Prove that, $ \cos \theta, \cos 2\theta \cos 2^2\theta....\cos 2^{n-1} \theta = \large\frac{\sin 2^n \theta}{2^n \sin \theta}$, for all $n \in N$ by using the principle of mathematical induction.

asked May 6, 2014 by thanvigandhi_1

0 answers

Prove that for all $n \in N$ \[\] $\cos \alpha+ \cos ( \alpha + \beta ) + \cos ( \alpha + 2 \beta )+...+ \cos ( \alpha + (n-1) \beta )$ \[\] $ = \large\frac{ \cos \bigg( \alpha + \bigg( \Large\frac{n-1}{2} \bigg) \beta \bigg) \sin \bigg( \Large\frac{n \beta}{2} \bigg)}{\sin \Large\frac{\beta}{2}}$ by using principle of mathematical induction.

asked May 6, 2014 by thanvigandhi_1

0 answers

A sequence $d_1, d_2, d_3...$ is defined by letting $d_1=2$ and $d_k=\large\frac{d_{k-1}}{k}$ for all natural numbers $k \geq 2$. Show that $d_n = \large\frac{2}{n!}$ for all $n \in N$ by using principle of mathematical induction.

asked May 6, 2014 by thanvigandhi_1

0 answers

A sequence $b_0, b_1, b_2...$ is defined by letting $b_0=5$ and $b_k=4+b_{k-1}$ for all natural numbers $k $. Show that $b_n = 5+4n$ for all natural number $n$ using mathematical induction.

asked May 6, 2014 by thanvigandhi_1

0 answers