A particle is projected from the ground with an initial speed $\upsilon $ at an angle $\theta $ with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is
$\frac{\upsilon }{2}\sqrt {1 + 2\,\,{{\cos }^{2\,}}\theta } $
$\frac{\upsilon }{2}\sqrt {1 + {{\cos }^{2\,}}\theta } $
$\frac{\upsilon }{2}\sqrt {1 + 3\,\,{{\cos }^{2\,}}\theta } $
$\upsilon \,\cos \,\theta $
An object is projected from ground with speed $20 \,m / s$ at angle $30^{\circ}$ with horizontal. Its centripetal acceleration one second after the projection is .......... $m / s ^2$ [Take $g=10 \,m / s ^2$ ]
A shell is fired from a fixed artillery gun with an initial speed $u$ such that it hits the target on the ground at a distance $R$ from it. If $t_1$ and $t_2$ are the values of the time taken by it to hit the target in two possible ways, the product $t_1t_2$ is
A body is projected from the ground at an angle of $45^{\circ}$ with the horizontal. Its velocity after $2s$ is $20 \,ms ^{-1}$. The maximum height reached by the body during its motion is $m$. (use $g =10\, ms ^{-2}$ )
Two particles are projected from the same point with the same speed at different angles $\theta _1$ and $\theta _2$ to the horizontal. They have the same range. Their times of flight are $t_1$ and $t_2$ respectively.
Two stones are projected so as to reach the same distance from the point of projection on a horizontal surface. The maximum height reached by one exceeds the other by an amount equal to half the sum of the height attained by them. Then, angle of projection of the stone which attains smaller height is $........$