Question

A cannon is shooting emergency packets to people stranded on the roof of a flooded building of height H = 104 meters relative to the cannon, the corner of which is located a distance D = 53 meters from the cannon. It is desired that the incoming packets are flying tangent to the roof as shown so that they land gently with as little impact as possible and slide along to a stop.

Find the initial speed v0 and at what angle è (in radians) the cannon should be aimed to achieve the above scenario.

Answer 1

vertical problem (time and speed same as 104 meter fall):
v = Vi - 9.81 t
0 = Vi - 9.81 t
t = Vi/9.81
104 = (1/2) g t^2
104 = (1/2) (9.81)(Vi^2/9.81^2)
Vi^ = 2 * 9.81 * 104
Vi = 45.2 m/s

horizontal problem (constant speed)
t = Vi/9.81 = 4.61 seconds
u = 53/4.61 = 11.5 m/s

tan (angle) = 45.2/11.5
so angle up from horizontal = 75.7 degrees

speed = sqrt (45.2^2 + 11.5^2)
= 46.6 m/s