Inside a starship at rest on the earth, a ball rolls off the top of a horizontal table and lands a distance D from the foot of the table. This starship now lands on the unexplored Planet X. The commander, Captain Curious, rolls the same ball off the same table with the same initial speed as on earth and finds that it lands a distance 2.76 D from the foot of the table. What is the acceleration due to gravity on Planet X?

Solution 15E Step 1: 0 This problem can be considered as a projectile motion fired at an angle of 0 grom a height of “h”. So, x0= 0and y = o which are the horizontal and vertical displacements of the ball. Again, x = v0t --------------(1) 2 and y = h 1/2 gt -----------------(2) When the ball reaches the bottom, the vertical displacement can be set to zero. So, 2 y = h 1/2 gt = 0 2 h = 1/2 gt t = gh----------------(3) This is the time required for the ball to reach the ground. Step 2: From equation (1), we can deduce “t” as a function of x, t = x/v -----------------(4) 0 Let’s put this value in equation (2), y = h 1/2 gt = h 1/2 × g × ( ) . v0 Again by setting y = 0, we can get a very useful result which will tell us about the horizontal range. I.e; 2 h 1/2 × g × (v) = 0 0 x 2 h = 1/2 × g × ( )0 x = 2hv ---------------(5) g 0