A particle is aimed at a mark, which is in the horizontal plane through the point of projection, falls a meters short of it when the elevation is a and goes beyond it b meters too far when the elevation is 3. Show that if the velocity of projection in each case be the same, then the proper elevation, 0, is a sin 28 +b sin 2a a +b 1 0 = =s Question 2: (a) A projectile started from O at an elevation a. After t seconds its position appeared to have an elevation 3 as seen from O. Prove that the initial velocity was gt cos B 2sin (a – B) (b) A stone is projected with velocity v and elevation 0 from a point O on level ground so as to hit a mark P on a wall whose distance from O is a the height of P above the ground being b. Prove that 20 (a sin 0 cos 0 – b cos² 0) = ga² Also prove that the requisite velocity of projection is least when 0 = +;, where a is the elevation of P as seen from O.
A particle is aimed at a mark, which is in the horizontal plane through the point of projection, falls a meters short of it when the elevation is a and goes beyond it b meters too far when the elevation is 3. Show that if the velocity of projection in each case be the same, then the proper elevation, 0, is a sin 28 +b sin 2a a +b 1 0 = =s Question 2: (a) A projectile started from O at an elevation a. After t seconds its position appeared to have an elevation 3 as seen from O. Prove that the initial velocity was gt cos B 2sin (a – B) (b) A stone is projected with velocity v and elevation 0 from a point O on level ground so as to hit a mark P on a wall whose distance from O is a the height of P above the ground being b. Prove that 20 (a sin 0 cos 0 – b cos² 0) = ga² Also prove that the requisite velocity of projection is least when 0 = +;, where a is the elevation of P as seen from O.
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Transcribed Image Text:A particle is aimed at a mark, which is in the horizontal plane through the point of
projection, falls a meters short of it when the elevation is a and goes beyond it b meters
too far when the elevation is B. Show that if the velocity of projection in each case be
the same, then the proper elevation, 0, is
1
0 = sin
a sin 2B + b sin 2a
a + b
Question 2:
(a) A projectile started from O at an elevation a. After t seconds its position appeared
to have an elevation B as seen from O. Prove that the initial velocity was
gt cos B
2sin (a – B)
(b) A stone is projected with velocity v and elevation 0 from a point O on level ground
so as to hit a mark P on a wall whose distance from O is a the height of P above the
ground being b. Prove that
2v (a sin 0 cos 0 – b cos? 0) = ga?
Also prove that the requisite velocity of projection is least when 0 = +, where a
is the elevation of P as seen from O.
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