Welcome to the article 1 During a fireworks display a shell is shot into the air with an initial speed of 80 0 m s at an angle of. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!
Answer :
The height at which the shell explodes is 233.48 meters, the time between the launch and the explosion is 6.91 seconds, and the horizontal displacement when the shell explodes is 125.32 meters.
Physics of Fireworks Projectile
To calculate the height at which the shell explodes (maximum height), we use the formula for the vertical motion under gravity, where the initial vertical velocity is given by vy = v0sin(θ) and the acceleration is due to gravity (g = 9.8 m/s2, downwards).
(a) Calculating the Height at Which the Shell Explodes
Using the initial vertical velocity of 70.0 m/s and the angle of 75.0°, vy = 70sin(75°) = 67.68 m/s. The shell will reach its highest point when its vertical velocity is zero. At this point, the vertical displacement (y) is the maximum height:
0 = vy2 - 2gy
0 = (67.68 m/s)2 - 2(9.8 m/s2)y
y = (67.68 m/s)2 / (2 x 9.8 m/s2)
y = 233.48 m
(b) Time Passed Between Launch and Explosion
The time to reach the highest point is the time taken for the vertical velocity to become zero due to gravity, calculated using t = vy / g:
t = 67.68 m/s / 9.8 m/s2
t = 6.91 s
(c) Horizontal Displacement of the Shell When it Explodes
Horizontal displacement (horizontal range) is calculated by multiplying the horizontal velocity with the time in the air. The initial horizontal velocity is vx = v0cos(θ) = 70cos(75°) = 18.13 m/s. The horizontal displacement is:
x = vx x t
x = 18.13 m/s x 6.91 s
x = 125.32 m
Thank you for reading the article 1 During a fireworks display a shell is shot into the air with an initial speed of 80 0 m s at an angle of. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Brahmana