Question

A small dingy is floating up to a pirate’s ship full of would be boarders. He angles his cannon downward at -15 degrees while 3.0m above the water. He fires his cannon at 95 m/s. The small boat of unfortunate crewmen is 20 m away. Do they survive their foolhardy errand?(please show work)

Answer 1

Speed of the cannon is 95 m/s

now we will find its two components

speed in horizontal direction is

`v_x = 95 cos15`

`v_x = 91.76 m/s`

speed in vertical direction is

`v_y = 95 sin(-15)`

`v_y = -24.6 m/s`

now the time taken by the cannon to reach the water surface will be find out by using kinematics

`\Delta y = v_y * t + (1)/(2) at^2`

`-3 = -24.6 * t - (1)/(2)9.8 * t^2`

`4.9t^2 + 24.6 t - 3 = 0`

By solving above quadratic equation

`t = 0.12 s`

now in the same time the horizontal distance moved by the cannon

`d_x = v_x * t`

`d_x = 91.76 * 0.12`

`d_x = 10.93 m`

Since the distance of crewmen is 20 m so it will definitely safe as cannon will hit at distance 10.93 m