A particle is projected from the ground with | vedclass

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

Question

(B) Given the formulas: $R = \frac{u^2 \sin 2	heta}{g}$,$H = \frac{u^2 \sin^2 	heta}{2g}$,and $T = \frac{2u \sin 	heta}{g}$.Since $u$ is constant,w

Vedclass · Accepted Answer

$R$ will first increase then decrease while $H$ and $T$ both will increase

Vedclass · Answer

(B) Given the formulas: $R = \frac{u^2 \sin 2	heta}{g}$,$H = \frac{u^2 \sin^2 	heta}{2g}$,and $T = \frac{2u \sin 	heta}{g}$.Since $u$ is constant,we analyze the trigonometric functions as $	heta$ varies from $30^o$ to $60^o$.For $R$: The term $\sin 2	heta$ varies from $\sin 60^o = \frac{\sqrt{3}}{2} \approx 0.866$ to $\sin 120^o = \frac{\sqrt{3}}{2} \approx 0.866$,passing through $\sin 90^o = 1$ at $	heta = 45^o$. Thus,$R$ increases until $45^o$ and then decreases.For $H$: The term $\sin^2 	heta$ increases monotonically as $	heta$ increases from $30^o$ to $60^o$ (since $\sin 30^o = 0.5$ and $\sin 60^o \approx 0.866$). Thus,$H$ increases.For $T$: The term $\sin 	heta$ increases monotonically as $	heta$ increases from $30^o$ to $60^o$. Thus,$T$ increases.Therefore,$R$ first increases then decreases,while $H$ and $T$ both increase.

Similar Questions

$A$ boy is moving with a constant speed $v$ on a small trolley towards a distant circle as shown in the figure. $A$ point mass is moving on the circle with a constant speed $v$. What is the frequency of change in the magnitude of the relative velocity of the point mass,as observed by the boy?

The second's hand of a watch has $6\, cm$ length. The speed of its tip and the magnitude of the difference in velocities of its tip at any two perpendicular positions will be respectively:

The velocity of a body at time $t = 0$ is $10\sqrt{2} \, m/s$ in the north-east direction and it is moving with an acceleration of $2 \, m/s^2$ directed towards the south. The magnitude and direction of the velocity of the body after $5 \, s$ will be

$A$ particle is performing uniform circular motion. If $\theta$,$\omega$,$\alpha$,and $a$ are its angular displacement,angular velocity,angular acceleration,and centripetal acceleration respectively,then which of the following is '$WRONG$'? ($v$ is its linear velocity)

$A$ body of mass $2 \, kg$ has an initial velocity of $3 \, m/s$ along $OE$ and it is subjected to a force of $4 \, N$ in a direction perpendicular to $OE$. The distance of the body from $O$ after $4 \, s$ will be ........... $m$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module