# Numerical Problems : Kinematics

#### LEVEL – I

Q:1. A cricketer hits a ball from the ground level with a velocity vo = (20i^ + 10j^ ) m/sec. Find the velocity of the ball at t = 1 sec, from the instant of projection (g = 10 m/sec2 ).

[ Ans: 20i^  ]

Q:2. A body is projected vertically up with a speed Vo . Find the magnitude of time average velocity of the body during its ascent.

[ Ans: Vo/2 ]

Q:3. A bomb is released from an aeroplane flying with a horizontal velocity of magnitude 100 m/sec at an altitude of 1 km. What is the displacement during the time of its flight ?

[ Ans: 1732 m ,  tan-1(0.707) ]

Q:4. A football player kicks the football so that it will have a ” hang time ” (time of flight) of 5s and lands 50 m away. If the ball leaves the playe’s foot 1.5m above the ground, what is its initial velocity (magnitude and direction)? (g = 10 m/sec2 )

[ Ans: 26.64 m/s, 67.96° ]

Q:5. A rocket is fired vertically up from the ground with a resultant vertical acceleration of 10 m/s2 . The fuel is finished in 1 minute and it continues to move up
(a) what is the maximum height reached ?
(b) After how much time from then will the maximum height be reached ? (Take g = 10 m/s2 )

[ Ans: (a) 36 km     (b) 1 minute ]

Q:6. A ball is falling from the top of a cliff of height h with an initial speed V. Another ball is simultaneously projected vertically up with the same speed. When do they meet ?

[ Ans: h/2V ]

Q:7. If an object travels one-half its total path in the last second of its fall from rest, find (a) the time and (b) the height of its fall. Explain the physically unacceptable solution of the quadratic time equation.

[ Ans: (a) 3.4 sec  (b) 57m ]

Q:8. A particle starts moving due east with a velocity v1 = 5 m/sec. for 10 sec. and turns to north with a velocity v2 =10 m/sec. for 5 sec. Find the average velocity of the particle during 15 sec. from starting.

[ Ans: 5√2/3 due north of east ]

Q:9. A particle is moving with a speed Vo in a circular path of radius R. Find the ratio of average velocity to its instantaneous velocity when the particle describes an angle θ (< π/2) .

Ans: $\displaystyle \frac{v_{av}}{v} = \frac{2 sin (\theta/2)}{\theta}$

Q:10. To a man moving due east with a speed v in a rain, the rain appears to fall vertically. If he changes his speed by a factor n, the rain appears to fall at an angle θ to vertical. Find the speed of the rain.

Ans: $\displaystyle v_r = v (\sqrt{1 + n^2 cot^2 \theta})$

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