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A Cricketer Can Throw a Ball to a Maximum Horizontal Distance of 100 M. How Much High Above the Ground Can the Cricketer Throw the Same Ball? - CBSE (Science) Class 11 - Physics

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Question

A cricketer can throw a ball to a maximum horizontal distance of 100 m. How much high above the ground can the cricketer throw the same ball?

Solution 1

R_"max" = 100 m

`Since `R_"max" = v^2/g => 100 = v^2/g`

Using equation of motion

`v^2 - u^2 = 2as`

Here, v = 0, a = -g, `s = R_"max"` = 100 m

`:.(0)^2 -u^2 = 2(-g) xx s`

`=> s = 1/2 u^2/g`

Since u = v

`:.s = 1/2 v^2/g = 1/2 xx 100 = 50 m`

Solution 2

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°, i.e., θ = 45°.

The horizontal range for a projection velocity v, is given by the relation:

`R = (u^2sin2theta)/g`

`100 = u^2/g sin 90^@`

`u^2/g = 100`  ..(i)

The ball will achieve the maximum height when it is thrown vertically 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 = -2gH`

`H=1/2xxu^2/g = 1/2xx100 = 50 m`

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Physics Textbook for Class 11 (2018 to Current)
Chapter 4: Motion in a Plane
Q: 16 | Page no. 87
Solution A Cricketer Can Throw a Ball to a Maximum Horizontal Distance of 100 M. How Much High Above the Ground Can the Cricketer Throw the Same Ball? Concept: Projectile Motion.
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