A spring loaded gun is set up on a laboratroy table top so that the end of the g

Question

A spring loaded gun is set up on a laboratroy table top so that the end of the gun is 30 cm above the table top and the gun is fired at an angle of 60 degrees above the horizontal. A plastic ball, fired from this spring loaded gun, has a muzzle velocity of 350 cm/ sec.

Part a) Determine the x- and y-components of the initial velocity of the ball.

Part b) Determine the maximum height above the table top that the ball will reach in cm.

Part c) How far (in cm) will the ball travel before hitting the table top? Assume that the table top is long enough that the ball will strike the table top no matter how far it goes.

Part d) What is the velocity at its highest point?

Explanation / Answer

v = 350 cm/s = 350/100 = 3.5 m/s

theta = 60o

(a) vx = v*cos 60 = 1.75 m/s

vy = v*sin 60 = 3.03 m/s

(b) Maximum height of projectile,

H = v2sin2theta / 2g

H = 3.52sin260 / 2*9.8

H = 0.46875 m

Above table top,

H = 0.3 + 0.46875

H = 0.76875 m

(c) Distance covered,

0 = 0.3 + 3.03t - 4.9t2

solving the quadrartic equation

t = 0.7052 sec

Therefore,

x = vxt

x = 1.75*0.7052

x = 1.234 m

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