# NCERT Physics Class 11 Exemplar Ch 4 Motion in A Plane Part 5

35 A cricket fielder can throw the cricket ball with a speed. If he throws the ball while running with speed u at an angle 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 at which he should throw the ball that would maximise the horizontal range as found in (iii).

(e) How does for maximum range change if?

(f) How does in (v) compare with that for

Ans:

(a)

(b)

(c)

(d)

(e) .

.

(f)

36 Motion in two dimensions, in a plane can be studied by expressing position, velocity and acceleration as vectors in Cartesian co-ordinates where and are unit vector along x and y directions, respectively and and are corresponding components of A. Motion can also be studied by expressing vectors in circular polar co-ordinates as where and are unit vectors along direction in which and ‘’ are increasing.

(a) Express and in terms of and.

(b) Show that both andare unit vectors and are perpendicular to each other.

(c) Show that where

and

(d) For a particle moving along a spiral given by , where (unit), find dimensions of ‘a’.

(e) Find velocity and acceleration in polar vector representation for particle moving along spiral described in (d) above.

Ans:

and

37 A man wants to reach from A to the opposite corner of the square C (Fig. 10). The sides of the square are 100 m. A central square of is filled with sand. Outside this square, he can walk at a speed 1 m/s. In the central square, he can walk only at a speed of What is smallest value of for which he can reach faster via a straight path through the sand than any path in the square outside the sand?

Ans:

37 Consider the straight line path APQC through the sand.

Time taken to go from A to C via this path

The shortest path outside the sand will be ARC.

Time taken to go from A to C via this path

For

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