A cricketer can throw a ball to a maximum horizontal distance of 100 m . How much high above (in m )

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3-2.Motion in Plane

medium

A cricketer can throw a ball to a maximum horizontal distance of $100\; m$. How much high above (in $m$) the ground can the cricketer throw the same ball ?

$40$

$50$

$60$

$100$

Solution

Maximum horizontal distance, $R=100 \,m$ The cricketer will only be able to throw the ball to the maximum horizontal distance when the angle of projection is $45^{\circ},$ i.e., $\theta=45^{\circ}$ The horizontal range for a projection velocity $v$, is given by the relation

$R=\frac{u^{2} \sin 2 \theta}{g}$

$100=\frac{u^{2}}{g} \sin 90^{\circ}$

$\frac{u^{2}}{g}=100$

The ball will achieve the maximum height when it is throwertically upward. For such motion, the final velocity $v$ is zero at the maximum height $H$ Acceleration, $a=-g$

Using the third equation of motion

$v^{2}-u^{2}=-2 g H$

$H=\frac{1}{2} \times \frac{u^{2}}{g}=\frac{1}{2} \times 100=50 \,m$

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Given that $u_x=$ horizontal component of initial velocity of a projectile, $u_y=$ vertical component of initial velocity, $R=$ horizontal range, $T=$ time of flight and $H=$ maximum height of projectile. Now match the following two columns.

Column $I$ Column $II$

$(A)$ $u_x$ is doubled, $u_y$ is halved $(p)$ $H$ will remain unchanged

$(B)$ $u_y$ is doubled $u_x$ is halved $(q)$ $R$ will remain unchanged

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Column $I$	Column $II$
$(A)$ $u_x$ is doubled, $u_y$ is halved	$(p)$ $H$ will remain unchanged
$(B)$ $u_y$ is doubled $u_x$ is halved	$(q)$ $R$ will remain unchanged
$(C)$ $u_x$ and $u_y$ both are doubled	$(r)$ $R$ will become four times
$(D)$ Only $u_y$ is doubled	$(s)$ $H$ will become four times

A cricketer can throw a ball to a maximum horizontal distance of $100\; m$. How much high above (in $m$) the ground can the cricketer throw the same ball ?

Solution

Similar Questions

Two bodies are thrown up at angles of $45^o $ and $60^o $, respectively, with the horizontal. If both bodies attain same vertical height, then the ratio of velocities with which these are thrown is

The ceiling of a long hall is $25\; m$ high. What is the maximum horizontal distance that a ball thrown with a speed of $40\; m/ s$ can go without hitting the ceiling of the hall ?

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