Final answer:
A basketball player must leave the floor with an initial vertical velocity of approximately 4.43 m/s to reach a height of 1.0 m using the kinematic equations for motion.
Step-by-step explanation:
To determine the velocity at which a basketball player leaves the floor to reach a height of 1.0 m, we can use the kinematic equation for motion under constant acceleration (gravity in this case). The equation we'll use is:
v^2 = u^2 + 2as
where:
- v is the final velocity (0 m/s at the peak of the jump)
- u is the initial velocity (the velocity we're trying to find)
- a is the acceleration (-9.81 m/s2, since gravity is acting downward)
- s is the displacement (1.0 m)
Rearranging the formula to solve for u, we have:
u = sqrt(v^2 - 2as)
Substituting the known values, we get:
u = sqrt(0 - 2*(-9.81 m/s2)*1.0 m)
u = sqrt(19.62 m2/s2)
u = 4.43 m/s
Thus, the basketball player must leave the floor with an initial vertical velocity of about 4.43 m/s to reach a height of 1.0 m.