To determine how long it would take for the ball to reach the ground, we can use the formula for the time of flight of a projectile:
t = sqrt((2 * h) / g),
where: t is the time of flight, h is the initial height of the ball, and g is the acceleration due to gravity (approximately 9.8 m/s²).
Substituting the given values into the formula:
t = sqrt((2 * 4) / 9.8) ≈ 0.9 seconds.
Therefore, it would take approximately 0.9 seconds for the ball to reach the ground.
Now, to calculate the horizontal distance the ball can move until it lands, we can use the formula for horizontal distance:
d = v * t,
where: d is the horizontal distance, v is the horizontal velocity, and t is the time of flight.
Substituting the given values:
d = 4 m/s * 0.9 s ≈ 3.6 meters.
Therefore, the ball can move approximately 3.6 meters horizontally until it lands.