A wooden block of mass 10   g m is dropped from the top of a tower 100   m high. Simultaneously, a bullet of mass 10   g m is fired from the foot of the tower vertically upwards with a velocity of 100   m   s - 1 . If the bullet is embedded in it, how high will it rise above the tower before it starts falling? g = 10   m   s - 2

Step-by-step solution

Block and bullet will collide after 1   s at height 95   m from ground. V e l o c i t y   o f   b l o c k   b e f o r e   c o l l i s i o n = g t = 10   m   s - 1 V e l o c i t y   o f   b u l l e t   b e f o r e   c o l l i s i o n = u – g t = 90   m   s - 1 from conservation of linear momentum, m – 10 + m 90 = 2   m v ′   ⇒   v ′ = 40   m   s - 1 Thus height raised by the combined mass h =