Is that symmetric?

Classical Mechanics Level 2

Lying on his back, a boy can throw a ball up to a maximum height of $10\text{ m}$ . Still lying on his back, what is the maximum horizontal distance that the boy can throw the ball?

Assume that he throws the ball with the same speed in either situation.

10\text{ m}

20\sqrt2\text{ m}

10\sqrt2\text{ m}

20\text{ m}

4 solutions

Akhil Bansal
Oct 30, 2015

When boy throws the ball vertically upwards,
$H_{\text{max}} = \dfrac{v_{0}^{2}}{2g}$ $10 * 2 g = v_{0}^{2}$

When boy throws the ball in horizontal direction,
$R = \dfrac{v_{0}^{2}\sin(2\theta)}{g}$ $R_{max} = \dfrac{20 g}{g}$ $R_{max} = 20 m$

$\color{#624F41}{\text{Notations used}}$ : $\text{H}_{max}$ = maximum height , $v_{0}$ = initial velocity with which ball is thrown , g = acceleratipn due to gravity , R = horizontal range.

Could you explain this low $R = \dfrac{u^2\sin(2\theta)}{g}$ and where $\theta$ located exactly? , and what is the acceleration value at horizontal range?

Refaat M. Sayed - 5 years, 7 months ago

This is a common formula used to find horizontal distance of a projectile.and $\theta$ is angle between velocity vector and horizontal.So, when $\theta = 45$ , horizontal range is maximim,

Akhil Bansal - 5 years, 7 months ago

question is worded wrong throwing horizontally means angle is 0 degrees from horizontal, so above solution does not apply

Iqbal Mohammad - 5 years, 7 months ago

Please read the question again... It is no where written that ball hsas to be thrown horizontally... Question is asking for maximum horizontal distance.

Akhil Bansal - 5 years, 7 months ago

Abhijeet Verma
Oct 30, 2015

Even after seeing so many assumptions in physics, i have always wondered why this question has never been answered as infinite!

Infinite... How?

Akhil Bansal - 5 years, 7 months ago

Assuming smooth horizontal surface.

SIDDHARTH SAHA - 5 years, 7 months ago

infinite is correct answer as no counter force exist in horizontal direction and condition of throwing is "Still lying on his back, " so angle of elevation is 0

Iqbal Mohammad - 5 years, 7 months ago

@Iqbal Mohammad – Your argument is flawed. Once the ball covers a quarter of Earth's circumference, all of the gravitational counter force acts in the horizontal direction(co-ordinate axes attached to boy's frame of reference). Your argument gives the impression that the ball would continue along horizontal direction into space to an infinite distance.

SIDDHARTH SAHA - 5 years, 7 months ago

@Siddharth Saha – Hey, the ball will start moving in circular motion around the centre of the earth and the gravitational force will be the centripetal force(assuming earth to be spherical).

Abhijeet Verma - 5 years, 7 months ago

@Iqbal Mohammad – Even if you consider a seemingly flat patch on the earth's surface, I'm not sure why you limited the "no counter force effect" only to angle of projection 0°. You could also assume no K.E. loss on bouncing off earth's surface and extend the "effect" to projection at 89°.

SIDDHARTH SAHA - 5 years, 7 months ago

To focus upon and test the concept of projectile motion, we ignore the practical complexities in such sums, like air resistance or the physics after ball strikes the ground. So, we only observe the ball till the moment it touches the ground.

SIDDHARTH SAHA - 5 years, 7 months ago

OO duh- we have no coefficient for friction

Joshua Coddington - 5 years, 7 months ago

Siva Prasad
Nov 7, 2015

It is a projectile motion... so many confused with the situation are separate or 0 angle so on.. the question mentions is is it symmetric... ans is 20m using trajectory eqns

there will be no acceleration along horizontal.. if consider both situations are separate.. it will have no meaning in it and ball moves forever then..

Anton Mark Casia
Nov 5, 2015

The answer should be infinite.

Given the fact the the boy is still lying down, the height of elevation would be zero and it would just seem that we would be letting it roll on the ground. If we assume that there is no friction, the ball would continue rolling forever at a constant velocity.

Is that symmetric?

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