A projectile of mass 0.882 kg is shot from a cannon. The end of the cannon’s bar

Question

A projectile of mass 0.882 kg is shot from a cannon. The end of the cannon’s barrel is at height 6.6 m, as shown in the gure. The initial velocity of the projectile is 8.1 m/s. The projectile rises to a maximum height of y above the end of the cannon’s barrel and strikes the ground a horizontal distance x past the end of the cannon’s barrel. x 8.1 m/s 49 y 6.6m Determine the vertical component of the initial velocity at the end of the cannon’s barrel, where the projectile began its trajectory. The acceleration of gravity is 9.8 m/s2 . Answer in units of m/s. 007 (part 2 of 7) 10.0 points Determine the maximum height y the projectile achieves after leaving the end of the cannon’s barrel. Answer in units of m. 008 (part 3 of 7) 10.0 points Determine the time it takes for the projectile to reach its maximum height. Answer in units of s. 009 (part 4 of 7) 10.0 points How long does it take the projectile to hit the ground? Answer in units of s. 010 (part 5 of 7) 10.0 points Find the magnitude of the velocity vector when the projectile hits the ground. Answer in units of m/s. 011 (part 6 of 7) 10.0 points Find the magnitude of the angle (with respect to horizontal) the projectile makes when impacting the ground. Answer in units of . 012 (part 7 of 7) 10.0 points Find the range x of the projectile. Answer in units of m.

Explanation / Answer

Vertical component , Voy = 8.1 Sin49 = 6.1 m/s

b)

Yo = initial position = 6.6 m

Ymax = final position

Vf = final velocity at the maximum height = 0 m/s

using the equation

Vfy2 = Voy2 + 2 a (Ymax - Yo )

02 = (6.1)2 + 2 (-9.8) (Ymax - 6.6)

Ymax = 8.6 m

c)

Vfy = Voy + a t

0 = 6.2 + (-9.8) t

t = 0.63 sec

d)

t' = time taken to hit the ground

Yf = final position = 0

using the equation

Yf = Yo + Voy t' + (0.5) a t'2

0 = 6.6 + (6.1) t' + (0.5) (-9.8) t'2

t' = 1.94 sec

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