On level ground a shell is fired with an initial velocity of 83.7 m/s at 50.8 ab

Question

On level ground a shell is fired with an initial velocity of 83.7 m/s at 50.8 above the horizontal and feels no appreciable air resistance.

A) Find the horizontal and vertical components of the shell's initial velocity.

B) How long does it take the shell to reach its highest point?

C) Find its maximum height above the ground.

D) How far from its firing point does the shell land?

E) At its highest point, find the horizontal and vertical components of its acceleration.

F) At its highest point, find the horizontal and vertical components of its velocity.

Explanation / Answer

(A)
Horizontal Component of the shell's initial velocity , Vx = 83.7 * cos(50.8) = 52.9 m/s
Vertical component of the shell's initial velocity, Vy = 83.7 * sin(50.8) = 64.86 m/s

(B)
v = u - a*t
At max height, v = 0
t = u/a
t = 64.86/9.8 s
t = 6.62 s
Time it take the shell to reach its highest point, t = 6.62 s

(C)
v^2 = u^2 - 2*a*s
At max height, v = 0
s = u^2/2*a
s = 64.86^2/ (2*9.8) m
s = 214.6 m
Max Height above the ground, s = 214.6 m

(D)
Total time taken by shell to reach ground, t = 2 * 6.62 s = 13.24 s

Horizontal distance travelled in this time, s = 13.24 * 52.9 m
Far from its firing point does the shell land = 700.4 m

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