Consider the following situation: A firework shoots off at an angle of theta_0 =
ID: 1411924 • Letter: C
Question
Consider the following situation: A firework shoots off at an angle of theta_0 = 53 degree at a speed pf v_0 = 20 m/s. At the apex of the firework's flight it explodes into two pieces, say one if blue and the other is green. The green firework leaves the explosion at an angle of theta_G = 37 degree with a speed of 15 m/s. The total mass of the firework had a mass of 1 kg, the green piece had a mass of 0.7 kg and the blue piece had a mass of 0.3 kg. The explosion was generated by a negligible amount of black powder. Calculate the height at which the firework explodes. Calculate the vertical and horizontal velocity of the firework at the apex of its flight. Calculate the horizontal and vertical velocity of the blue piece after the explosion. Calculate the horizontal distance where the green piece lands on the ground relative to where the firework was launched. Calculate the horizontal distance where the blue piece lands on the ground relative to where the firework was launched. How far apart did the green and blue pieces land from one another?Explanation / Answer
(a)
Initial Vertical velocity = 20 * sin(53) = 16.0 m/s
Vertical velocity at max height = 0
Acceleration = 9.8 m/s^2 donwards
v^2 = u^2 - 2*a*s
0 = 16^2 - 2*9.8*s
s = 13.1 m
Height at which firework explodes, s = 13.1 m
(b)
At the apex of flight,
Vertical Velocity = 0
Horizontal velocity = 20 * cos(53) = 12.0 m/s
(c)
Horizontal velocity of blue piece, vh
Using Momentum conservation,
12.0 * 1 = 0.7 * 15 * cos(37) + 0.3 * vh
vh = 12.1 m/s
Vertical velocity of blue piece, vy
Using Momentum conservation,
0 = 0.7 * 15 * sin(37) + 0.3 * vy
vy = 21.1 m/s
(d)
First let us calculate the time taken to reach max height,
v = u - a*t
0 = 16 - 9.8 * t
t = 1.63 s
Horizontal distance travelld, s = 1.63 * 12.0 = 19.56 m
Now, time taken by Green piece to reach ground,
S = u*t + 1/2*at^2
- 13.1 = 15 * sin(37) * t - 1/2 *9.8 * t^2
t = 2.80 s
Horizontal distance travelled by Green piece, = 15 * cos(37)* 2.80 = 33.5 m
Total distance travelled = 19.56 + 33.5 = 53.1 m