Q29. A stone is projected from level ground with speed u and at an angle q with horizontal. Somehow the acceleration due to gravity (g) becomes double (that is 2g) immediately after the stone reaches the maximum height and remains same thereafter. Assume direction of acceleration due to gravity always vertically downwards. Find
(i) The total time of flight of particle
(ii) The horizontal range of particle
(iii) The angle ϕ which the velocity vector of stone makes with horizontal just before hitting the ground.
Q30. The velocity 'v' of a particle moving along straight line is given in terms of time t as v = 3 (t2 – t) where t is in seconds and v is in m/s. Find
(i) The distance travelled by particle from t = 0 to t = 2 seconds
(ii) The displacement of particle from t = 0 to t = 2 seconds
(iii) The speed is minimum after t = 0 second at instant of time-
Q32. An observer having a gun observes a remotely controlled balloon. When he first noticed the balloon, it was at an altitude of 800 m and moving vertically upward at a constant velocity of 5 m/s. The horizontal displacement of balloon from the observer is 1600 m. Shells fired from the gun have an initial velocity of 400 m/s at a fixed angle ѐ (sin ѐ = 3/5 and cos ѐ = 4/5). The observer having gun waits (for some time after observing the balloon) and fires so as to destroy the balloon.
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Assume g = 10 m/s2. Neglect air resistance. Find
(i) The flight time of the shell before it strikes the balloon is
(ii) The altitude of the collision above ground level is
(iii) After noticing the balloon, the time for which observer having gun waits before firing the shell is
Q33. A particle which is initially (at t = 0) at rest at the origin, is subjected to an acceleration with x-and y-components as as shown. After time t = 5, the particle has no acceleration.
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(i) What is the magnitude velocity of the particle at t = 2 seconds?
(ii) What is the magnitude of average velocity of the particle between t = 0 and t = 4 seconds?
(iii) When is the particle at its farthest distance from the y-axis?
Q33. A particle which is initially (at t = 0) at rest at the origin, is subjected to an acceleration with x-and y-components as as shown. After time t = 5, the particle has no acceleration.
