Final answer:
The flea reaches a height of approximately 0.00507 meters when it jumps straight up with an acceleration of 1000 m/s² over a distance of 0.50 mm.
Step-by-step explanation:
Given that the flea accelerates at 1000 m/s² over a distance of 0.50 mm, we can use the kinematic equation to find the final velocity:
v² = u² + 2as
Where v is the final velocity, u is the initial velocity (which is 0 since the flea jumps straight up), a is the acceleration, and s is the distance.
Plugging in the values, we have:
v² = 0 + 2(1000)(0.50x10^-3)
Simplifying, we get:
v² = 0.001
Taking the square root of both sides, we find that the final velocity (v) is approximately 0.0316 m/s.
Next, we can use the equation for vertical motion to find the height the flea reaches:
v² = u² + 2as
Where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity (approximately 9.8 m/s²), and s is the height.
Plugging in the values, we have:
(0.0316)² = 0 + 2(-9.8)s
Simplifying, we get:
s = 0.00507 m
Therefore, the flea reaches a height of approximately 0.00507 meters.