a missile is launched off a jet fighter travelling 300 meters per second. it accelerated with a constant acceleration of 100 meters per second. when it has traveled 5000 meters what will its velocity be?
To find the velocity of the missile after it has traveled 5000 meters, we can use the equation of motion:
v^2 = u^2 + 2as
Where:
v = final velocity of the missile
u = initial velocity of the missile
a = acceleration of the missile
s = displacement or distance traveled by the missile
Given:
u = 300 m/s (initial velocity)
a = 100 m/s^2 (acceleration)
s = 5000 m (displacement)
First, we need to find the final velocity. Rearranging the equation, we have:
v^2 = u^2 + 2as
Substituting the known values:
v^2 = (300 m/s)^2 + 2 * 100 m/s^2 * 5000 m
Calculating further:
v^2 = 90000 m^2/s^2 + 1000000 m^2/s^2
v^2 = 1090000 m^2/s^2
Taking the square root of both sides to find v:
v ≈ √1090000 m/s
v ≈ 1044.03 m/s
Therefore, when the missile has traveled 5000 meters, its velocity will be approximately 1044.03 m/s.