2. A spring loaded gun is used to launch a ping pong ball (mass 4g) at an angle

Question

2. A spring loaded gun is used to launch a ping pong ball (mass 4g) at an angle of 50 degrees with the horizontal. The spring has constant k 40N/m and the initial compression of the spring was 3cm. Ignoring air resistance, how far does the ping pong travel if it is launched from the ground (lands at the same height it was shot from)? What is the maximum height that it reaches? How long does it take to complete its trajectory? 2. A spring loaded gun is used to launch a ping pong ball (mass 4g) at an angle of 50 degrees with the horizontal. The spring has constant k 40N/m and the initial compression of the spring was 3cm. Ignoring air resistance, how far does the ping pong travel if it is launched from the ground (lands at the same height it was shot from)? What is the maximum height that it reaches? How long does it take to complete its trajectory?

Explanation / Answer

0.5kx^2 = 0.5mv^2

v^2 = kx^2 / m

= 40*0.03^2 / 0.004

= 9

v = 3 m/s

Y = Uy*t -0.5gt^2

0 = 3sin 50 *t - 0.5*9.8*t^2

t = 0.47 s

X = Ux*t

= 3 cos 50 * 0.47 = 0.9 m

maximum height

Vy^2 = Uy^2 - 2gHmax

Hmax = Uy^2 / 2g = (3sin 50)^2 / 2*9.8 = 0.27 m

time taken = 0.47 s

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