From the window of a building, a ball is tossed from a height y0 above the groun
ID: 1883842 • Letter: F
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
Explanation / Answer
(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
===============================
(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
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