If a stone is to hit a point which is at a ho | vedclass

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

Question

(B) The equations of motion for a projectile are:Horizontal displacement: $d = (u \cos 	heta) t$Vertical displacement: $h = (u \sin 	heta) t - \frac

Vedclass · Accepted Answer

$\frac{d}{\cos 	heta} \sqrt{\frac{g}{2(d 	an 	heta - h)}}$

Vedclass · Answer

(B) The equations of motion for a projectile are:Horizontal displacement: $d = (u \cos 	heta) t$Vertical displacement: $h = (u \sin 	heta) t - \frac{1}{2} g t^2$From the horizontal equation,we find the time of flight to reach distance $d$:$t = \frac{d}{u \cos 	heta}$Substitute this expression for $t$ into the vertical displacement equation:$h = (u \sin 	heta) \left( \frac{d}{u \cos 	heta} ight) - \frac{1}{2} g \left( \frac{d}{u \cos 	heta} ight)^2$$h = d 	an 	heta - \frac{g d^2}{2 u^2 \cos^2 	heta}$Rearranging to solve for $u^2$:$\frac{g d^2}{2 u^2 \cos^2 	heta} = d 	an 	heta - h$$u^2 = \frac{g d^2}{2 \cos^2 	heta (d 	an 	heta - h)}$Taking the square root of both sides:$u = \frac{d}{\cos 	heta} \sqrt{\frac{g}{2(d 	an 	heta - h)}}$

$(A)$ Range	$(i)$ $\frac{P}{Q}$
$(B)$ Maximum height	$(ii)$ $P$
$(C)$ Time of flight	$(iii)$ $\frac{P^2}{4 Q}$
$(D)$ Tangent of projection	$(iv)$ $\left(\sqrt{\frac{2}{g Q}}\right) P$

If a stone is to hit a point which is at a horizontal distance $d$ and at a vertical height $h$ above the point from where the stone is launched,what is the initial speed $u$ if the stone is launched at an angle $\theta$?

Similar Questions

$A$ stone is projected at an angle $\theta$ with velocity $u$. If it executes nearly a circular motion at its maximum point for a short time,the radius of the circular path will be ($g=$ acceleration due to gravity).

$A$ particle moves in the $xy$ plane with a constant acceleration $g$ in the negative $y$-direction. Its equation of motion is $y = ax - bx^2$,where $a$ and $b$ are constants. Which of the following are correct?

$A$ stone is projected at an angle of $30^{\circ}$ to the horizontal. The ratio of the kinetic energy of the stone at the point of projection to its kinetic energy at the highest point of its flight will be:

When a ball is thrown with a velocity of $50 \ m s^{-1}$ at an angle $30^{\circ}$ with the horizontal,it remains in the air for how many seconds? (Take $g = 10 \ m s^{-2}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module