A rookie quarterback throws a football with an initial upward velocity component

Question

A rookie quarterback throws a football with an initial upward velocity component of 17.0 m/s and a horizontal velocity component of 19.7 m/s . Ignore air resistance.

Problem 3.18 Part A How much time is required for the football to reach the highest point of the trajectory? A rookie quarterback throws a football with an initial upward velocity component of 17.0 m/s and a horizontal velocity component of 19.7 m/s Ignore air resistance Take the free fall acceleration to be g = 9.80 m/s Submit My Answers Give Up Incorrect; Try Again; 3 attempts remaining Part B How high is this point? Take the free fall acceleration to be g= 9.80 m/s2 Submit My Answers Give Up Incorrect; Try Again; 4 attempts remaining Part C How much time (after it is thrown) is required for the football to return to its original level? Take the free fall acceleration to be g= 9.80 m/82 Submit My Answers Give Up Part D How far has it traveled horizontally during this time? Take the free fall acceleration to be g = 9.80 m/82

Explanation / Answer

A)

At the highest point, vy must be zero

Before that, it was moving up, and after that it is moving down, so it must momentarily stop at that point

Vy = Voy - gt

here, Voy = 17 m/s, g = 9.8 m/s^2

0 = 17 - 9.8*t

t = 17/9.8

t = 1.7345 s

b)

y = yo + Voyt = 1/2gt^2

here, yo = 0 , Voy = 17 m/s , t = 1.7345 s, g = 9.8 m/s^2

y = (17 x 1.7345) - (0.5 x 9.8 x (1.7345)^2)

y = 29.49 - 14.74

y = 14.75 m

c)

y = yo + Voyt - 1/2gt^2

here, y = 0 , yo = 0

Voyt - 1/2gt^2 = 0

1/2gt^2 - Voyt = 0

t(1/2gt - Voy) = 0

from this equation,

t = 0 or t = 2voy / g

t = (2 x 17) / 9.8

t = 3.47 s

d)

X = Xo + Vxt

here, Xo = 0 , Vx = 19.7 m/s, t = 3.47 s

X = (19.7 m/s x 3.47 s)

X = 68.36 m

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