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Excellent human jumpers can leap straight up to a height of 120 cm off the ground. To reach this height, with what speed would a person need to leave the ground?

We know that when an object, including a human, reaches their highest point, the vertical component of the speed would be 0, since they will have stopped going up but not yet begun coming down at that point. Having made that observation, this question can be solved by using one of the kinematic equations of motion in the vertical direction, taking upwards as positive.

We have the following information:
a = acceleration (due to gravity) = -9.8 m/s²
v = final speed = 0 m/s
d = distance = 120 cm = 1.20 m
u = initial velocity = ?

v² = u² + 2ad. Since v = 0, this becomes u² = -2ad = -2*-9.8*1.2 = 23.52, and taking the square root gives an initial velocity of 4.85 m/s.

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