A rocked is fired from te ground as a projectile. At the top of its trajectory,

Question

A rocked is fired from te ground as a projectile.  At the top of its trajectory, at a horizontal distance of 260m from the launch point,, the rocket breaks into two pieces: one fragmentn having 1/3 of the mass of the original rocket and the remaining piece having 2/3 of the original mass.  The smaller pieve falls straight down to the ground beneath the break-up point while the larger continues.  At what horizontal distance from the lauch point does the larger fragment lat? (Hint: by one-dimension kinematics, both pieces must his the ground at the same time.)

Explanation / Answer

the hroizontal and vertical components of the mass at thehighest point are w1 = w * cos and w2 = w * sin the smaller piece falls straight down to the ground beneaththe break-up point while the larger continues therefore weget w * cos = m1 * g or cos = (m1 * g/w) = (m1 * g/m *g) = (m1/m) m1 = (m/3) or = cos-1((m/3)/m) = cos-1(1/3)= 70.5o the range of the projectile is R = (u2 * sin(2)/g) or u = [(R * g)/sin(2)]1/2-----------(1) R = 260 m and g = 9.8 m/s2 the total time of flight of the larger mass is t = (2u * sin/g) ------------(2) therefore,the horizontal distance from the lauch point doesthe larger fragment fall is S = ut + (1/2)gt2 the values of u and t are obtained from equations (1) and(2). the values of u and t are obtained from equations (1) and(2).

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