A student performs a ballistic pendulum experiment using an apparatus similar to that shown in Figure 9.11b. She obtains the following average data: h = 8.68 cm, m1 = 68.8 g, and m2 = 263 g. The symbols refer to the quantities in Figure 9.11a.
(a) Determine the initial speed v1A of the projectile.
(b) The second part of her experiment is to obtain v1A by firing the same projectile horizontally (with the pendulum removed from the path), by measuring its final horizontal position x and distance of fall y (Fig. P9.65). Show that the initial speed of the projectile is related to x and y through the relation
v1A = x/√2y/g
What numerical value does she obtain for v1A based on her measured values of x = 257 cm and y = 85.3 cm? What factors might account for the difference in this value compared to that obtained in part (a)?

Figure P9.65