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 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
- [JEE MAIN 2019]
- A
$2R/g$
- B
$R/4g$
- C
$R/g$
- D
$R/2g$
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- [AIIMS 2006]
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$(c)$ what is the distance (horizontal range) from the point of projection at which the ball will land ?
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$(f)$ how does $\theta $ in $(v)$ compare with that for $u=0$ $($ i.e., $45^{o})$ ?
A cricket fielder can throw the cricket ball with a speed $v_{0} .$ If he throws the ball while running with speed $u$ at an angle $\theta$ to the horizontal, find
$(a)$ the effective angle to the horizontal at which the ball is projected in air as seen by a spectator
$(b)$ what will be time of flight?
$(c)$ what is the distance (horizontal range) from the point of projection at which the ball will land ?
$(d)$ find $\theta$ at which he should throw the ball that would maximise the horizontal range as found in $(iii)$.
$(e)$ how does $\theta $ for maximum range change if $u > u_0$. $u =u_0$ $u < v_0$ ?
$(f)$ how does $\theta $ in $(v)$ compare with that for $u=0$ $($ i.e., $45^{o})$ ?
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