Show your work on free-response questions. Be sure to use proper units and signi

Question

Show your work on free-response questions. Be sure to use proper units and significant figures in your final answers. Organization and neatness count, too. use red ink please reserve that color for grading 1. A golf ball is hit in a high arc on level eround. Its initial velocity is 25.0 m/s at 62.0 ve the horizontal. Ignore air resistance. a.(2 pts. What are the vertical and horizontal components of the ball's initial velocity, v.? Show your work. b. (3 pts.) Show that the ball will land 4.50 s after it is struck Showlexplain your work completely. c (4 pts.) What is the ball's total velocity (magnitude and direction) at 3.00 s? Show your work.

Explanation / Answer

a)Vx = V cos(theta)

Vx = 25 x cos62 = 11.74 m/s

Vy = V sin(theta)

Vy = 25 x sin62 = 22.07 m/s

Hence, Vx = 11.74 m/s ; Vy = 22.07 m/s

b)we know that,

v^2 = u^2 + 2 a S

S = 22.07^2/2 x 9.8 = 24.85 m

max height = S = 24.85 m

S = ut + 1/2 at^2

24.85 = 22.07 t - 4.9 t^2

4.9t^2 - 22.07 t + 24.85 = 0

t = 2.25 ; but total time is:

T = 2 x T = 2 x 2.25 = 4.5 s

Hence, total time = T = 4.5 s

c)at t = 3 s

Vy = Viy + at

Vy = 22.07 - 9.8 x 3 = -7.33 m/s

V = sqrt [ (-7.33)^2 + (11.74)^2] = 13.84 m/s

theta = tan-1 (-7.33/11.74) = -32 deg

Hence, theta = 32 deg and lvl = 13.84 m/s

d)Maximum height,

we know that,

v^2 = u^2 + 2 a S

S = 22.07^2/2 x 9.8 = 24.85 m

max height = S = 24.85 m

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