Question

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

Answer 1

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.