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 of1.05m above the muzzles of the cannons. Clown A is launched at?A=72.0

Explanation / Answer

let 2 clowns meet after time t at position [x, 1.05] and [6.40 -x, 1.05] angle of projection of 2nd is (- p) x = 9.5 cos 72 *t 6.40 - x = v0b cos ( -p) *t = v0b cos p *t adding v0b cos p = [6.40 - 9.5 cos 72 * t] / t ----------- (1) -------------------- 1.05 = 9.5 sin 72 *t - 0.5 gt^2 1.05 = - vob sin p *t - 0.5 gt^2 -------------------------------- vob sin p = - 9.5 sin 72 = - 9.04 ------------- (2) ===================== solving 1.05 = 9.5 sin 72 *t - 4.9t^2 4.9 t^2 - 9.04 t + 1.05 = 0 t = 1.72 or t = 0.13 (1) gives v0b cos p = 0.78 or v0b cos p = 46.29 ------------- (3) two possibilities > whether collision took place when first was rising or falling at 1.05 m ---------------- from (1) & (2) squaring/adding vob^2 = 9.04^2 + 0.78^2 >>> vob = 9.07 m/s or vob^2 = 9.04^2 + 436.29^2 >>> vob = 47.16 m/s --------------------------------------

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