a bullet is fired vertically upward from a gun at a velocity of 150m/s.taking g to be 10m/s calculate the gretest heigt reached and at what time and the time the bullet will enter the gun and at what velocity
V = Vo + g*Tr = 0.
Tr = -Vo/g = -150/-10 = 15 s. = Rise time.
Tf = Tr = 15 s.
Tr+Tf = 15 + 15 = 30s. = Time in flight.
V = Vo + g*Tf = 0 + 10*15 = 150 m/s. = Final velocity.
h = Vo*Tr + 0.5g*Tr^2.
Vo = 150 m/s.
Tr = 15 s.
g = -10 m/s^2.
h = ?.
To calculate the greatest height reached and the time it takes for the bullet to reach it, we need to apply the equations of motion.
First, we can find the time it takes for the bullet to reach its maximum height using the equation:
v = u + at
where:
v = final velocity (0 m/s at the top)
u = initial velocity (150 m/s)
a = acceleration (gravity, -10 m/s^2 since it is against the upward direction)
t = time
Rearranging the equation:
t = (v - u) / a
t = (0 - 150) / -10
t = 15 seconds
So, it takes 15 seconds for the bullet to reach its maximum height.
Next, we can calculate the maximum height using the kinematic equation:
h = u*t + (1/2)*a*t^2
where:
h = height
u = initial velocity (150 m/s)
t = time (15 seconds)
a = acceleration (gravity, -10 m/s^2)
h = 150 * 15 + (1/2) * (-10) * (15)^2
h = 2250 - 1125
h = 1125 meters
Therefore, the greatest height reached by the bullet is 1125 meters.
Now, to calculate the time it takes for the bullet to enter the gun again, we can use the following equation:
v = u + at
where:
v = final velocity (0 m/s)
u = initial velocity (150 m/s)
a = acceleration (gravity, -10 m/s^2)
t = time
Rearranging the equation:
t = (v - u) / a
t = (0 - 150) / -10
t = 15 seconds (same as before)
So, it takes 15 seconds for the bullet to fall back into the gun.
Lastly, to calculate the velocity at which the bullet enters the gun, we can use the equation:
v = u + at
where:
v = final velocity
u = initial velocity (150 m/s)
a = acceleration (gravity, -10 m/s^2)
t = time (15 seconds)
v= 150 + (-10) * 15
v = 150 - 150
v = 0 m/s
Therefore, the velocity at which the bullet enters the gun is 0 m/s.