A projectile of mass M-10.5 kg is launched over level ground at a speed 19.1 and

Question

A projectile of mass M-10.5 kg is launched over level ground at a speed 19.1 and at an angle of 30.0 degrees above the horizontal. At the instant that the projectile is at what would be its highest point it explodes into two pieces; after the explosion there is a piece of mass m1-5.3kg which has a vertical component of velocity of 9.1 m, and a second piece of mass m2 which moves downwards. The explosion does not change the horizontal component of the velocity of either piece How far from the launch point does m2 land? Answer in meters. AVI

Explanation / Answer

let's start with finding the height at which the explosion takes place

h = ( 19.1 sin 30 )^2/ ( 2x g) = 4.653 m apprx

we will conserve momentum along the y axis

10.5 ( 0) = 5.3 ( 9.1) + 5.2 (v)

v ( initial vertical velocity of mass m2) = 9.275 m/s

time for m2 to fall on the ground

-4.653 = -9.275 (t) - 1/2 (9.8) t^2

4.9 t^2 +9.275 t - 4.653=0

t = - 9.275 +- sqroot ( 9.275^2 +91.2 )/ 9.8=

t= 0.412 seconds

time of half flight = 19.1 sin 30 / 9.8 = 0.974 sec

hx ( horizontal distance) = 0.412( 19.1 cos 30) + 0.974 ( 19.1 cos 30 ) = 16.54 (1.386)=22.92 m apprx

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