On level ground a shell is fired with an initial velocity of 39.0 m/s at 67.0 ab

Question

On level ground a shell is fired with an initial velocity of 39.0 m/s at 67.0 above the horizontal and feels no appreciable air resistance

Part A. Find the horizontal and vertical components of the shell's initial velocity. Enter your answers numerically separated by a comma.

Part B. How long does it take the shell to reach its highest point? Express your answer using three significant figures.

Part C. Find its maximum height above the ground. Express your answer using three significant figures.

Part D. How far from its firing point does the shell land? Express your answer using three significant figures.

Part E. At its highest point, find the horizontal and vertical components of its acceleration. Enter your answers numerically separated by a comma.

Part F. At its highest point, find the horizontal and vertical components of its velocity. Enter your answers numerically separated by a comma.

Explanation / Answer

Initial velocity v = 39.0 m / s
angle ,theta = 67.0 degrees
(A). the horizontal component of the shell's initial velocity = v cos 67.0 = 15.24 m / s
vertical component of shells' initial velocity = v sin 67.0 = 35.90 m / s

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(B). time taken to reach maximu height t = v sin (theta ) / g
t = 3.66 s

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(C). Maximum height H = ( v sin(theta) )^ 2/ 2g
= 65.69 m

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(D). Required distance =2* v^ 2 *sin(theta)*cos(theta) / g
= 111.53 m

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(E). Horizontal component of accleraton = 0
vertical component of accleration = g = -9.8 m / s^ 2

(0 , -9.8)

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(F). Horizontal component of velocity at required point = v cos (theta ) = 15.24 m / s
vertical compoent of velocity at required point = 0

(15.24 , 0)

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