A gun that is spring-loaded shoots an object horizontally. The initial height of the gun is h=5 cm and the object lands 20 cm away. What is the gun's muzzle velocity?
Do i use something like v=sqr(k)/m*x. I am getting something like 3.2m/s, is this somewhat correct at all.
the choices I have are
a. 2.0 m/s
b. 1.0 m/s
c. 3.2 m/s
d. 4.9 m/s
e. 3.9 m/s
A gun that is spring-loaded shoots an object horizontally. The initial height of the gun is h=5 cm and the object lands 20 cm away. What is the gun's muzzle velocity?
the choices I have are
a. 2.0 m/s
b. 1.0 m/s
c. 3.2 m/s
d. 4.9 m/s
e. 3.9 m/s
The time to impact derives from h = Vot + gt^2/2 where h = the vertical height traversed = 5cm = .05m, Vo = the initial vertical speed = 0, t = the time to fall the 5cm distance and g = the acceleration due to gravity = 9.8m/sec^2 = 980cm/sec^2.
Therefore, 5 = (0)t + 490t^2 from which t = sqrt(5/490) = .101 sec.
For the object to travel 20cm horizontally, its initial velocity had to be V = D/T = 20/.101 = 198cm/sec =1.98.m/s or ~2m/sec.
To find the muzzle velocity of the spring-loaded gun, we can use the equation of motion for projectile motion.
The equation for the horizontal distance covered by a projectile is given as:
x = v * t
where x is the horizontal distance, v is the initial velocity, and t is the time of flight.
In this case, the object lands 20 cm away, which is equivalent to 0.2 meters (converting from cm to meters). The initial height of the gun is h = 5 cm, which is equivalent to 0.05 meters.
Now, we need to find the time of flight to determine the muzzle velocity. The time of flight can be determined using the equation of motion for vertical motion:
h = (1/2) * g * t^2
where g is the acceleration due to gravity (approximately 9.8 m/s^2) and t is the time of flight.
Since the vertical motion starts from rest (initial velocity is zero), the equation can be simplified to:
h = (1/2) * g * t^2
0.05 = (1/2) * 9.8 * t^2
0.05 = 4.9 * t^2
t^2 = 0.05 / 4.9
t^2 = 0.0102
t ≈ √0.0102
t ≈ 0.101 seconds (approx.)
Now that we have the time of flight, we can substitute it back into the horizontal distance equation:
x = v * t
0.2 = v * 0.101
v = 0.2 / 0.101
v ≈ 1.98 m/s (approx.)
So, the muzzle velocity of the gun is approximately 1.98 m/s.
Comparing this with the given choices, we see that the closest option is 2.0 m/s, which is choice a.
Therefore, the correct answer to the question is a. 2.0 m/s.