A cannonball is fired horizontally off the edge of a 10 m high cliff, with a spe

Question

A cannonball is fired horizontally off the edge of a 10 m high cliff, with a speed of 20 m/s.

a.) Find the time it takes for the cannonball to hit the ground.

b.) How far from the base of the cliff does the ball land?

c.) Find the total velocity vector of the cannonball just before it hits the ground.

d.) If you wanted to make the cannonball's flight time to be exactly 1.6 seconds, then you could dig a hole in the ground below the cliff (at the appropriate location.) How deep would this hole need to be?

Explanation / Answer

h =10 m , ux =20 m/s

uy =0, ay =9.8 m/s^2 , ax =0

(a) From kinematic equation along verticla direction

h = uy+(1/2)ayt^2

10 =0+(0.5*9.8)t^2

t = 1.429 s

b) from kinematic equaiton along horizontal direction

x= uxt+(1/2)axt^2

x = (20*1.429) +0

x = 28.58 m

c) In horizontal direction final veloicty =initial velocity

vx = 20 m/s

in vertical direction

vy =uy+ayt

vy = (9.8*1.429)

vy =14 m/s

final velocity vector v = 20i+ 14 j

d) t =1.6 s

form kinematic equations

H = (1/2)gt^2 = 0.5*9.8*1.6*1.6

H = 12.544 m

depth of hole d =H-h = 12.544-10

depth of hole d = = 2.544 m

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