A rocket, initially at rest, is fired vertically with an upward acceleration of 10 m/s2. At an altitude of 500 m, find its velocity.
1000 m/s
500 m/s
100 m/s
10 m/s
V^2 = Vo^2 + 2g*h
V^2 = 0 + 20*500 = 10,000
V = 100 m/s.
To find the velocity of the rocket at an altitude of 500 m, we can use the equations of motion.
First, let's find the time it takes for the rocket to reach an altitude of 500 m. We can use the second equation of motion:
s = ut + (1/2)at^2
Where:
s = displacement (500 m)
u = initial velocity (0 m/s)
a = acceleration (10 m/s^2)
t = time
Rearranging the equation, we get:
t^2 = 2s/a
t^2 = (2 * 500 m) / (10 m/s^2)
t^2 = 100
t = 10 s
Now that we have the time, we can find the velocity of the rocket using the first equation of motion:
v = u + at
Where:
v = final velocity (unknown)
u = initial velocity (0 m/s)
a = acceleration (10 m/s^2)
t = time (10 s)
Substituting the values into the equation, we get:
v = (0 m/s) + (10 m/s^2 * 10 s)
v = 100 m/s
Therefore, the velocity of the rocket at an altitude of 500 m is 100 m/s.