3.2 Two-Dimensional Motion 7. GP A student stands at the edge of a cliff and thr

Question

3.2 Two-Dimensional Motion 7. GP A student stands at the edge of a cliff and throws a -Yo = + 18.0 m/s stone horizontally over the edge with a speed of 18.0 m/s. The cliff is 50.0 m above a flat, horizontal beach as shown in Figure P3.7. (a) What are the coordinates of the initial posi- tion of the stone? (b) What are the components of the initial velocity? (c) Write the equations for the x- and y-components of the velocity of the stone with time. (d) Write the equations for the position of the stone 12 15 14 Figure P3.7 Unless otherwise noted, all content on this page is & Cengage Learning

Explanation / Answer

a) initial coardinates, xo = 0, yo = 50.0 m

b) vox = 18.0 m/s
voy = 0

c) vx = vox

vy = voy - g*t

d) x = vox*t

y = yo - (1/2)*g*t^2

e) let t is the time taken.

use, y = yo - (1/2)*g*t^2

0 = 50 - (1/2)*9.8*t^2

-50 = -(1/2)*9.8*t^2

t = sqrt(2*50/9.8)

= 3.19 s

f) vy = voy - g*t

= 0 - 9.8*3.19

= 31.3 m/s

vx = vox = 18.0 m/s

impact speed, v = sqrt(vx^2 +vy^2)

= sqrt(18^2 + 31.3^2)

= 36.1 m/s

angle of impact, theta = tan^-1(vy/vx)

= tan^-1(31.3/18)

= 60.1 degrees below horizontal

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