Suppose a 12.0 kg fireworks shell is shot into the air with an initial velocity

Question

Suppose a 12.0 kg fireworks shell is shot into the air with an initial velocity of 63.0 m/s at an angle of 80.0° above the horizontal. At the highest point of its trajectory, a small explosive charge separates it into two pieces, neither of which ignite (two duds). One 9.00 kg piece falls straight down, having zero velocity just after the explosion. Neglect air resistance (a poor approximation, but do it anyway).

(a) At what horizontal distance from the starting point does the 9.00 kg piece hit the ground?

(b) Calculate the velocity of the 3.00 kg piece just after the separation ?

(c) At what horizontal distance from the starting point does the 3.00 kg piece hit the ground?

Explanation / Answer

a) To reach the highest point in the trajectory,

the vertical velocity has to become zero ,

Initial vertical velocity = 63* sin 80 = 62.04288 m/s

Time taken to vertical velocity to become zero = 62.04288/9.8 = 6.3309 seconds

So distance travelled in horizontal direction during 6.3309 seconds = 63 * cos (80) * 6.3309 = 69.259 m

At what horizontal distance from the starting point does the 9.00 kg piece hit the ground = 69.259 m

b) Initial momentum = 12*63*cos(80) =131.278 Kg.m/s

Final momentum = momentum of 9 Kg particle + Momentum of 3 Kg particle

One 9.00 kg piece falls straight down, having zero velocity just after the explosion

So, momentum of 9 Kg particle =0

By conservatiuon of momentum

Initial momentum = Final momentum =131.278 Kg.m/s

Momentum of 3 Kg particle = 131.278 Kg.m/s

so, 3* velocity of 3 Kg particle = 131.278 Kg.m/s

velocity of 3 Kg particle = 43.759 m/s

the velocity of the 3.00 kg piece just after the separation = 43.759 m/s

c) The time taken for the 3 kg particle to come down = 6.3309 seconds

so horizontal distance travelled by the 3 Kg particle during 6.3309 seconds = 43.759* 6.3309 = 277.0338531 m

Total horizontal distance travelled = 277.0338531 + 69.259 = 346.2928531 m

At what horizontal distance from the starting point does the 3.00 kg piece hit the ground = 346.2928531 m

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