Question

A dart gun consists of a spring (k = 367 N/m) and a 25.0 g dart. When the dart is loaded into the gun, the spring is compressed 7.0 cm. The gun is aimed straight up and fired. a) How high does the dart go, ignoring air resistance of course? b) How fast is the dart going when it comes back down to the horizontal level at which it was fired?

Answer 1

Solution,

A)

Energy, E = 0.5 kx^2 = mgh

Height, h = kx^2/2 mg

h = (367 x 0.07^2)/(2 x 0.025 x 9.8) = 3.7 m

B)

Energy, E = 0.5 mv^2 = mgh

Velocity, v = sqrt(2gh) = sqrt(2 x 9.8 x 3.7) = 8.52 m/s

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