Consider a marble moving on a horizontal track with a speed of 10 meters per second( ignore friction and air resistance). the marble leaves the track and falls through the air to the ground a vertical distance of 1.5 meters.
how long does it take to for the marble to hit the ground?
you can ignore the horizontal speed of the marble (unless you want to find out far far it travels).
s = 1/2 at^2
1.5 = 1/2 * 9.8 t^2
t = 0.55 sec
To determine the time taken by the marble to hit the ground, we can use the concept of projectile motion and apply the equations of motion. The marble is moving horizontally with a constant speed, so we only need to consider the vertical motion.
First, let's calculate the time taken for the marble to fall a vertical distance of 1.5 meters. We can use the equation of motion for free fall:
h = (1/2) * g * t^2,
where h is the vertical distance (1.5 meters), g is the acceleration due to gravity (approximately 9.8 meters per second squared), and t is the time taken.
Rearranging the equation to solve for t, we get:
t^2 = (2 * h) / g,
t = sqrt((2 * h) / g).
Substituting the given values, we have:
t = sqrt((2 * 1.5) / 9.8),
t ≈ sqrt(0.3061),
t ≈ 0.5539 seconds (approximated to four decimal places).
Therefore, it takes approximately 0.5539 seconds for the marble to hit the ground.