Two seconds after projection,a projectile is | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the initial velocity be $u$ at an angle $	heta$ with the horizontal. The horizontal component is $v_x = u \cos 	heta$ and the vertical compo

Vedclass · Accepted Answer

$20 \sqrt{3} \, m/s, 60^o$

Vedclass · Answer

(B) Let the initial velocity be $u$ at an angle $	heta$ with the horizontal. The horizontal component is $v_x = u \cos 	heta$ and the vertical component is $v_y = u \sin 	heta$.At $t = 3 \, s$,the projectile is at its highest point,so $v_y = 0$. Thus,$u \sin 	heta - g(3) = 0$,which gives $u \sin 	heta = 3g = 30 \, m/s$ (taking $g = 10 \, m/s^2$).At $t = 2 \, s$,the vertical velocity is $v_y' = u \sin 	heta - g(2) = 30 - 20 = 10 \, m/s$.The horizontal velocity remains constant: $v_x = u \cos 	heta$.The direction is given by $	an 30^o = \frac{v_y'}{v_x} = \frac{10}{u \cos 	heta}$.Since $	an 30^o = \frac{1}{\sqrt{3}}$,we have $\frac{1}{\sqrt{3}} = \frac{10}{u \cos 	heta}$,so $u \cos 	heta = 10\sqrt{3} \, m/s$.The initial velocity magnitude is $u = \sqrt{(u \cos 	heta)^2 + (u \sin 	heta)^2} = \sqrt{(10\sqrt{3})^2 + (30)^2} = \sqrt{300 + 900} = \sqrt{1200} = 20\sqrt{3} \, m/s$.The angle $	heta$ is $	an 	heta = \frac{u \sin 	heta}{u \cos 	heta} = \frac{30}{10\sqrt{3}} = \frac{3}{\sqrt{3}} = \sqrt{3}$. Thus,$	heta = 60^o$.

Two seconds after projection,a projectile is travelling in a direction inclined at $30^o$ to the horizontal. After one more second,it is travelling horizontally. What is the magnitude and direction of its velocity at the initial point?

Similar Questions

In an atom,the order of increasing energy of electrons with quantum numbers $(i)$ $n=4, l=1$,$(ii)$ $n=4, l=0$,$(iii)$ $n=3, l=2$,and $(iv)$ $n=3, l=1$ is:

In adiabatic compression,the decrease in volume is associated with

If the decimal $0.d25d25d25\ldots$ is expressible in the form $n/27$,then $d+n$ must be

If $A$ is the areal velocity of a planet of mass $M$,its angular momentum is

Identify from the following,a hormone produced by the pituitary gland in both males and females but functional only in females.

Vedclass Test Series

Exam Paper Generator

Online Exam Module