A ball rolls off a desk at a speed of 3.0 m/s and lands .40 seconds later. How high is the desk
recall that s = 1/2 at^2 = 1/2 * 9.81 * 0.40^2 = 0.784 meters
The horizontal speed does not matter
To determine the height of the desk, we can use the equation for vertical motion, which relates the initial velocity, time, and gravitational acceleration to the height.
The equation for vertical motion is:
h = (v_initial * t) + (1/2) * g * t^2
Where:
h is the height of the desk,
v_initial is the initial velocity of the ball (in this case, it is 3.0 m/s),
t is the time taken for the ball to fall (in this case, it is 0.40 seconds), and
g is the acceleration due to gravity, which is approximately 9.8 m/s^2 on the Earth's surface.
Plugging in the given values into the equation:
h = (3.0 m/s * 0.40 s) + (1/2) * (9.8 m/s^2) * (0.40 s)^2
Simplifying the equation:
h = 1.20 m + 0.78 m
h = 1.98 m
Therefore, the height of the desk is approximately 1.98 m.