Two cannons are mounted as shown in the drawing and rigged to fire simultaneousl

Question

Two cannons are mounted as shown in the drawing and rigged to fire simultaneously. They are used in a circus act in which two clowns serve as human cannonballs. The clowns are fired toward each other and collide at a height of 1.05 m above the muzzles of the cannons. Clown A is launched at theta_A = 72.0 degree angle, with a speed v_0A = 8.50 m/s. The horizontal separation between the clowns as they leave the cannons is d = 6.40 m. Find the launch speed v_0B and the launch angle theta_B (>45.0 degree) for clown B. magnitude m/s direction degree

Explanation / Answer

along vertical

for A

yA = 1.05 m

yA = voA*sin72*t - 0.5*g*t^2

1.05 = (8.5*sin72*t)-(0.5*9.8*t^2)

t = 1.51 s

for B

yB = voB*sintheta*t - 0.5*g*t^2

1.05 = voB*sinthetaB*1.51 - 0.5*9.8*1.51^2

voB*sintheta = 8.1

along horizantal

xA = voA*cos72*t

xB = voB*costhetaB*t

xA + xB = voA*cos72*t + voB*costhetaB*t

6.4 = (8.5*cos72*1.51) + (voB*costhetaB*1.51)

voB*costheta = 1.61

voB = sqrt(8.1^2+1.61^2) = 8.26 m/s

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