A body is projected with a speed u m/s at an | vedclass

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

Question

(A) The initial kinetic energy at the point of projection $O$ is given by:$K = \frac{1}{2} mu^2$where $m$ is the mass of the body and $u$ is the initi

Vedclass · Accepted Answer

$30$

Vedclass · Answer

(A) The initial kinetic energy at the point of projection $O$ is given by:$K = \frac{1}{2} mu^2$where $m$ is the mass of the body and $u$ is the initial velocity of projection.At the highest point (i.e.,at maximum height $H$),the vertical component of velocity becomes zero,and the velocity is only the horizontal component:$v = u \cos \beta$Therefore,the kinetic energy at the highest point is:$K^{\prime} = \frac{1}{2} mv^2 = \frac{1}{2} m(u \cos \beta)^2 = \frac{1}{2} mu^2 \cos^2 \beta$According to the problem,the kinetic energy at the highest point is $\frac{3}{4}$ of the initial kinetic energy:$K^{\prime} = \frac{3}{4} K$Substituting the expressions:$\frac{1}{2} mu^2 \cos^2 \beta = \frac{3}{4} \left( \frac{1}{2} mu^2 \right)$$\cos^2 \beta = \frac{3}{4}$Taking the square root on both sides:$\cos \beta = \frac{\sqrt{3}}{2}$$\beta = \cos^{-1} \left( \frac{\sqrt{3}}{2} \right) = 30^{\circ}$

$A$ body is projected with a speed $u \ m/s$ at an angle $\beta$ with the horizontal. The kinetic energy at the highest point is $\frac{3}{4}$ of the initial kinetic energy. The value of $\beta$ is $....^{\circ}$

Similar Questions

The work functions for metals $A, B$ and $C$ are respectively $1.92\, eV, 2.0\, eV$ and $5\, eV$. According to Einstein's photoelectric equation,which of these metals will emit photoelectrons for an incident radiation of wavelength $4100\, \mathring{A}$?

$A$ vessel contains oil (density $= 0.8 \, g/cm^3$) over mercury (density $= 13.6 \, g/cm^3$). $A$ homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in $g/cm^3$ is

If $\log _{0.3}(x - 1) < \log _{0.09}(x - 1),$ then $x$ lies in the interval

In a standing wave on a string rigidly fixed at both ends:

$A$ horizontal tube of non-uniform cross-section has radii of $0.2\,m$ and $0.1\,m$ at points $P$ and $Q$ respectively. For streamline flow of an incompressible liquid, the rate of liquid flow is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module