a.) On planet #1 you drop a stone from rest, 80m above the ground and the stone

Question

a.) On planet #1 you drop a stone from rest, 80m above the ground and the stone hits the ground 10.2 seconds later what is the value of g for planet 1?

b.) On planet #2 you launch a projectile straight up from the ground at a speed of 30 m/s the projectile reaches maximum height of 584.0m before falling back to the ground. what is the value of g ?

c.) On planet #3 you fire a projectile horizontally from the edge of a vertical cliff 80m above the ground, with an initial speed of 55.0m/s. The projectile lands 980 m away from the base of the cliff what is the value of g?

d.) On planet #4 you fire a projectile from the ground at an initial speed of 40 m/s at an angle of 30 degrees above the horizontal. The projectile lands 402 m away from the launch point. what is the value of g?

e.) On planet #5 a stone is dropped from a height of 200 m above the ground and will hit the ground at 38.0 m/s what is the value of g?

Explanation / Answer

a)

along vertical

initial velocity = vo = 0

acceleration ay = -g

displacement y = -80 m

time = 10.2 s

from equation of motion

y= vo*t + 0.5*ay*t^2

-80 = 0 - 0.5*g*10.2^2

g = 1.54 m/s^2 <<<---------answer

_________

(b)

along vertical

initial velocity = vo = 30

acceleration ay = -g

displacement y = 584 m

from equation of motion

v^2 - vo^2 = 2*ay*y

0 - 30^2 = -2*g*584

g = 0.77 m/s^2 <<<---------answer

________

c)

along horizantal

x = v*t

t = x/v ........(1)

along vertical

initial velocity = vo = 0

acceleration ay = -g

displacement y = -80 m

time = ?

from equation of motion

y= vo*t + 0.5*ay*t^2

-80 = 0 - 0.5*g*(980^2/55^2)

g = 0.51 m/s^2

_____________

d)

along horizantal

x = vx*t =

402 = 40*cos30*t

t = 11.6 s

along vertical

total displacement = 0

y = voy*t + 0.5*ay*t^2

0 = (40*sin30)*11.6 - (0.5*g*11.6^2)

g = 3.45 m/s^2

____________

e)

along vertical

voy = 0

vy = -38 m/s

y = -200 m

vy^2 - voy^2 = 2*ay*y

38^2 - 0 = 2*g*200

g = 3.61 m/s^2

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