Question

From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 7.90 m/s and angle of 19.0° below the horizontal. It strikes the ground 6.00 s later.

(a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: y0. Assume SI units. Do not substitute numerical values; use variables only.)

xi =

yi =

(b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity.

vi, x = _______ m/s

vi, y = _______m/s

(c) Find the equations for the x- and y-components of the position as functions of time. (Use the following as necessary: y0 and t. Assume SI units.)

x =_____ m

y = ____m

(d) How far horizontally from the base of the building does the ball strike the ground?

_______m

(e) Find the height from which the ball was thrown.

______m

(f) How long does it take the ball to reach a point 10.0 m below the level of launching?

Please show work

Answer 1

(a)

xi = 0

along vertical

initial velocity voy = -vo*sintheta = -7.9*sin19

initial point yo = yi

final point after falling on earth y = 0

acceleration ay = -9.8 m/s^2

time taken t = 6 s

y - yo = voy*t + (1/2)*ay*t^2

0-yi = -7.9*sin19*6 - (1/2)*9.8*6^2

yi = 192 m

xi = 0 <<----------------ANSWER

yi = 192 m <<----------------ANSWER

==========================

(b)

vi, x = v*costheta = 7.9*cos19 = 7.47 m/s <<----------------ANSWER

along y direction

vi, y = -v*sintheta = -7.9*sin19 = -2.57 m/s <<----------------ANSWER

--------------------------

(c)

x = xo + vix*t + (1/2)*a*t^2

x = 0 + 7.47*t + 0

v = 7.47*t   <<<-------------answer

y = yo + viy*t + (1/2)*ay*t^2

y = 192 - 2.47*t - (1/2)*9.8*t^2

y = 192 - 2.47*t - 4.9*t^2   <<<-------------answer

================================

(d)

ball stike the ground after time 6 s

x = 7.47*6 = 44.82 m <<----------------ANSWER

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(e)

height h = yi = 192 m   <<<-------------answer

=======================

(f)

for y = y0 - 10= 192 - 10 = 182

182 = 192 - 2.47*t - 4.9*t^2

time t = 1.2 s <<<-------------answer