R1 = range of ball 1, R2 = range of ball 2
v1 = 1.9 m/s (velocity of ball 1), v2 = velocity of ball 2
h1 = 1.2 m (initial height of ball 1), h2 = 1.5 m (initial height of ball 2)
t1 = time it takes for ball 1 to fall, t2 = time it takes for ball 2 to fall
To start with, lets find out the time it will take for balls 1 and 2 to hit the ground...
Using constant acceleration kinematics, we find that:
and
solving for t1 and t2, we get:
and
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Now we can calculate the range of each ball...
Again, using basic kinematics (with no acceleration), we find the ranges to be:
R1 = v1 * t1 and R2 = v2 * t2
The problem specifies that R1 = R2, so we can set them equal to each other and solve for v2:
From this we can calculate that v2 = 1.7 m/s
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