Find the height from which you would have to drop a ball so that it would have a speed of 8.4 m/s just before it hits the ground.
To find the height from which you would have to drop a ball, we can use the equation for the final velocity of an object under free fall:
v² = u² + 2as
where:
v is the final velocity (8.4 m/s),
u is the initial velocity (0 m/s, as the ball is dropped),
a is the acceleration due to gravity on Earth (approximately 9.8 m/s²),
and s is the distance or height.
Rearranging the equation, we have:
s = (v² - u²) / (2a)
Substituting the given values, we get:
s = (8.4² - 0) / (2 * 9.8)
s = 70.56 / 19.6
s ≈ 3.6 meters
Therefore, the height from which you would have to drop the ball for it to have a speed of 8.4 m/s just before it hits the ground is approximately 3.6 meters.