A projectile is thrown with an initial velocity of $(a \hat{ i }+b \hat{ j }) ms ^{-1}$. If the range of the projectile is twice the maximum height reached by it, then

Four bodies $P, Q, R$ and $S$ are projected with equal velocities having angles of projection $15^{\circ}, 30^{\circ}, 45^{\circ}$ and $60^{\circ}$ with the horizontals respectively. The body having shortest range is

Three identical balls are projected with the same speed at angle $30^o, 45^o$ and $60^o$. Their ranges are $R_1 R_2$ and $R_3$ respectively. Then

A projectile fired at $30^{\circ}$ to the ground is observed to be at same height at time $3 s$ and $5 s$ after projection, during its flight. The speed of projection of the projectile is $.........\,ms ^{-1}$(Given $g=10\,m s ^{-2}$ )

A cricket ball is thrown at a speed of $28\; m /s$ in a direction $30^o$ above the horizontal. Calculate

$(a)$ the maximum height,

$(b)$ the time taken by the ball to return to the same level, and

$(c)$ the distance from the thrower to the point where the ball returns to the same level

An object is projected at an angle of $45^°$ with the horizontal. The horizontal range and the maximum height reached will be in the ratio.