The angle of projection for a projectile to have same horizontal range and maximum height is :
$\tan ^{-1}(2)$
$\tan ^{-1}(4)$
$\tan ^{-1}\left(\frac{1}{4}\right)$
$\tan ^{-1}\left(\frac{1}{2}\right)$
An insect trapped in a circular groove of radius $12 \;cm$ moves along the groove steadily and completes $7$ revolutions in $100\; s$.
$(a)$ What is the angular speed, and the linear speed of the motion?
$(b)$ Is the acceleration vector a constant vector ? What is its magnitude ?
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
Two projectiles are fired from the same point with the same speed at angles of projection $60^o$ and $30^o$ respectively. Which one of the following is true?
A cricketer can throw a ball to a maximum horizontal distance of $100 \,m$. With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball is ......... $m$
The maximum horizontal range of a projectile is $160\, m$. When the projectile is thrown with the same speed at an elevation of $30^o$ from the horizontal, it will reach to the maximum height of ......... $m$