A ball rolls horizontally off the top of a stairwaywith a speed of 1.52 m/s. The steps are 20.3 cm high and 20.3 cmwide. Which step does the ball hit first?

To solve this problem, we need to use the equations of motion.

Step 1: Convert all measurements to the same units. In this case, we'll use meters. So, the height and width of each step is 0.203 m.

Step 2: Determine the time it takes for the ball to fall vertically. We can use the equation of motion: h = 0.5gt^2, where h is the height, g is the acceleration due to gravity (9.8 m/s^2), and t is the time. Solving for t gives us t = sqrt(2h/g) = sqrt(2*0.203/9.8) = 0.203 seconds.

Step 3: Determine the horizontal distance the ball travels in this time. We can use the equation d = vt, where d is the distance, v is the velocity, and t is the time. Plugging in our values gives us d = 1.52 * 0.203 = 0.309 m.

Step 4: Compare the horizontal distance the ball travels to the width of the steps. Since 0.309 m is greater than 0.203 m, the ball will hit the second step first.