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A small ball is projected at an angle al...

A small ball is projected at an angle `alpha` between two vertical walls such that in the absence of the wall its range would have been `5d`. Given that all the collisions are perfectly elastic, find.
(a) maximum height atained by the ball.
(b) total number of collisions with the walls before the ball comes back to the ground, and
(c) point at which the ball finally falls. The walls are supposed to be very tall.

A

`(2u^(2) sin^(2) alpha)/(g)`

B

`(2u^(2) cos^(2) alpha)/(g)`

C

`(u^(2) sin^(2) alpha)/(2g)`

D

`(u^(2))/(2g)`

Text Solution

Verified by Experts

The correct Answer is:
C
Vertical component of velocity of the ball do not change after collision.
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Knowledge Check

  • Suppose a ball is projected with speed u at an angle alpha with horizontal. It collides at some distance with a wall parallel to y-axis. Let v_(x) and v_(y) be the components of its velocity along x and y-directions at the time of impact with wall. Coefficient of restitution between the ball and the wall is e . Component of its velocity along y -diection (common tangent) v_(y) will remain unchanged while component of its velocity along x -direction (common normal) v_(x) will become ev_(x) is opposite direction. The situation shown in the figure a small ball is projected at an angle alpha between two vertical walls such that in the absence of the wall its range would have been 5d . Given that all the collisions are perfectly elastic (for first and second problems), the walls are supposed to be very tall. The total time taken by the ball to come back to the ground (if collision is inelastic) is

    A
    `gt (2u sin alpha)/(g)`
    B
    `lt (2u sin alpha)/(g)`
    C
    `= (2u sin alpha)/(g)`
    D
    `= (2u cos alpha)/(g)`

  • Two balls each of mass m are moving with same velocity v on a smooth surface as shown in figure. If all collisions between the balls and balls with the wall are perfectly elastic, the possible number of collisions between the balls and wall together is

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    1
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    3
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    A
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    B
    `-5 ms^(-1)`
    C
    `1.0 ms^(-1)`
    D
    `-10 ms^(-1)`
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