NCERT Class 11 Physics Solutions: Chapter 3 – Motion in a Straight Line Part 5

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Question: 3.9

Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period T of the bus service and with what speed (assumed constant) do the buses ply on the road?

Answer:

  • Let V be the speed of the bus running between towns A and B.

  • Speed of the cyclist,

  • Relative speed of the bus moving in the direction of the cyclist

  • The bus went past the cyclist every 18 min i.e., (when he moves in the direction of the bus).

  • Distance covered by the bus

  • Since one bus leaves after every T minutes, the distance travelled by the bus will be equal to:

  • Both equations (i) and (ii) are equal.

  • Relative speed of the bus moving in the opposite direction of the cyclist

  • Time taken by the bus to go past the cyclist

  • From equations and , we get

  • Substituting the value of V in equation we get

Question 3.10:

A player throws a ball upwards with an initial speed of

(A) What is the direction of acceleration during the upward motion of the ball?

(B) What are the velocity and acceleration of the ball at the highest point of its motion?

(C) Choose the and to be the location and time of the ball at its highest point, vertically downward direction to be the positive direction of x-axis, and give the signs of position, velocity and acceleration of the ball during its upward, and downward motion.

(D) To what height does the ball rise and after how long does the ball return to the player’s hands? (Take and neglect air resistance).

Answer:

  • Irrespective of the direction of the motion of the ball, acceleration (which is actually acceleration due to gravity) always acts in the downward direction towards the centre of the Earth.

  • The direction of acceleration during the upward motion of the ball is downward.

  • At maximum height, velocity of the ball becomes zero. Acceleration due to gravity at a given place is constant and acts on the ball at all points (including the highest point) with a constant value i.e.,

  • , acceleration

  • During upward motion, the sign of position is positive, sign of velocity is negative, and sign of acceleration is positive. During downward motion, the signs of position, velocity, and acceleration are all positive.

  • For both up and down motions, for up and for down motion, throughout the motion

  • Initial velocity of the ball,

  • Final velocity of the ball, (At maximum height, the velocity of the ball becomes zero)

  • Acceleration,

  • From third equation of motion, height (s) can be calculated as:

  • From third equation of motion, height (s) can be calculated as:

  • Times of ascent Time of descent

  • Hence, the total time takes by the ball to return to the player’s hands