Numerical Problems 3.1: A helicopter is ascending vertically at a speed of 19.6 m/s. When it is a height of 156.8 m above the ground, a stone is dropped. How long does the stone take to reach the ground? (Ans. 8.0 s)

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Numerical Problems 3.3: A proton moving with the speed of 1.0 ｘ10⁷ m s⁻¹ passes through a 0.02 cm thick sheet of paper and emerges with speed of 2 ï½˜10⁶ m s⁻¹. Assuming uniform deceleration, find retardation and time taken to pass through the paper. Ans. (2.4 x 10¹⁷m s⁻², 3.3 x 10⁻¹¹s ) 

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Numerical Problems 3.4: Two masses m₁ and m₂ are initially at rest with a spring compressed between them. What is the ratio of their velocities after spring has been released.

(Ans: `\frac {v_1^'}{v_2^'}` = `\frac {m_2}{m_1}`)

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Numerical Problems 3.5: An amoeba of mass 1 ｘ10⁻¹² kg propels itself through water by blowing a jet of water through a tiny orifice. The amoeba ejects water with a speed of 1 ｘ10⁻⁴ m s⁻¹

at a rate of 1 ｘ10⁻¹³ kg s⁻¹. Assume that the water is continuously replenished so that the mass of the amoeba remains the same.
(a) If there were no force on amoeba other then the reaction force caused by the emerging jet, what would be the acceleration of the amoeba?
(b) If amoeba moves with constant velocity through water, what is force of surrounding water (exclusively of jet) on the amoeba? 
(Ans: 1.0 ｘ 10⁻⁵ m s⁻², 1.0 ｘ 10⁻¹⁷ N)

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Numerical Problems 3.6: A boy places a fire cracker of negligible mass in an empty can of 40 g mass. He plugs the end with a wooden block of mass 200 g. After igniting the fire cracker, he throws the can straight up. It explodes at the top of its path. If the block shoots out with a speed of 3 m s⁻¹, how fast will the can be going? 

(Ans: 15 m s⁻¹)

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Numerical Problems 3.7: An electron (m = 9.1 ｘ 10⁻³¹ kg) traveling at 2 ｘ 10⁷ m s⁻¹ undergoes a head on collision with a hydrogen atom (m = 1.67 ｘ 10⁻²⁷kg), which is initially at rest. Assume the collision to be perfectly elastic and motion to be a straight line, find the velocity of hydrogen atom. 

(Ans: 2.2 ｘ 10⁴ m s⁻¹)

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Numerical Problems 3.8: A truck weighing 2500 kg and moving with a velocity of 21 m s⁻¹ collides with stationary car weighing 1000 kg. The truck and the car move together after the impact. Calculate their common velocity.  

(Ans: 4.0 ï½˜ 10⁻⁶ T)

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Numerical Problems 3.9: Two blocks of masses 2 kg and 0.5 kg attached at two ends of a compressed spring. The elastic P.E. stored in the spring is 10 J. Find the velocities of the blocks if the spring delivers its energy to the blocks when released.  

(Ans: 1.4 m s⁻¹,  5.6 m s⁻¹)

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Numerical Problems 3.10: A football is thrown upward at an angle of 30 degree with respect to the horizontal. To throw a 40 m pass what must be the initial speed of the ball? (Ans: 21 m s⁻¹)

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Numerical Problems 3.11: A ball is thrown horizontal from a height of 10 m with velocity of 21 m s⁻¹. How far off will it hit the ground and with what velocity? 

(Ans: 30 m,  25 m s⁻¹)

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Numerical Problems 3.12: A bomber dropped a bomb at a height of 490 m. when its velocity along the horizontal was 300 Km h⁻¹.

(a) How long it was in air? 
(b) At what distance from the point vertically below the bomber at the instant the bomb was dropped, did it strike the ground?
 (Ans: 10s, 833 m)

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