If a missile is launched from a station 300 metres above sea level with an initial velocity of 500 m/s what is the height of the missile after 4 seconds
recall your basic equation of motion:
y = 300 + 500t - 4.9t^2
To find the height of the missile after 4 seconds, we need to use a kinematic equation that relates the initial velocity, time, and height.
The equation we'll use is:
h = h₀ + v₀t + (1/2)gt²
Where:
- h is the final height of the missile
- h₀ is the initial height of the missile above sea level (300 m in this case)
- v₀ is the initial velocity of the missile (500 m/s in this case)
- t is the time in seconds (4 seconds in this case)
- g is the acceleration due to gravity (approximately 9.8 m/s²)
Now let's substitute the values into the equation:
h = 300 + (500 × 4) + (1/2)(9.8)(4²)
Simplifying the equation:
h = 300 + 2000 + (1/2)(9.8)(16)
h = 300 + 2000 + (1/2)(156.8)
h = 2300 + 78.4
h ≈ 2378.4 meters
Therefore, the height of the missile after 4 seconds is approximately 2378.4 meters above sea level.