Three balls are launched simultaneously, as in the figure. The red ball is launc

Question

Three balls are launched simultaneously, as in the figure. The red ball is launched at an initial velocity directed at an angle above the horizontal. The blue ball is launched vertically with a speed of 10.1 m/s, and the yellow ball is launched horizontally with a speed of 4.70 m/s. The blue and red balls reach identical maximum heights and return to the ground at the same time, and the red ball returns to the ground to meet the yellow ball at the same place along the horizontal. Find (a) the launch speed v0 and (b) the launch angle for the red ball.

Explanation / Answer

Since vertical height reached by blue and red balls are same, their initial vertical velocities must be the same

vo sin = 10.1 m/s         (1)

Since horizontal distance covered by yellow and red balls are same, their initial horizontal velocities must be the same

vo cos = 4.70 m/s        (2)

Divide 1 and 2

tan = (10.1/4.70)

= 65o

Using value of in eq(1)

vo sin 65o = 10.1

vo = 11.14 m/s

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