Experiments on various alien planets, each with its own different g value (accel

Question

Experiments on various alien planets, each with its own different g value (acceleration due to gravity). We assume no air resistance for each example.

a) On a planet #1, you drop a stone from rest, 80 m above the ground, and the stone hits the ground 18.4 seconds later. What is the value of g for planet #1 (answer in m/s2)

b) On planet #2, you launch a projectile straight up from the ground at a speed of 30 m/s. The projectile reaches a maximum height of 509.0 m before falling back to the ground. What is the value of g for planet #2? (answer in m/s2)

c) On planet #3, you fire a projectile horixontally from the edge of a vertical cliff 80m above the ground, with an initial speed of 28.0 m/s. The projectile lands 194.0 m away from the base of the cliff. What is the value of g for planet #3? (answer in m/s2)

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 450.0 m away from the launch point. what is the value of g for planet #4? (answer in m/s2)

e) On plane #5, a stone dropeed from a height of 200 m above the ground will hit the ground at a speed of 61.0 m/s. What is the value of g for planet #5 (answer in m/s2)

Could you please include the formulas for each. Thank you!

Explanation / Answer

a) h = ut + 0.5*g1t^2

80 = 0*t + 0.5*g1*(18.4)^2

g1 = 0.4725 m/s^2

b) Hmax = u^2/2*g2

509 = 30^2/2*g2

g2 = 0.884 m/s^2

c) D = v*t

194 = 28*t

t = 6.92857 s

H = 0.5*g3*t^2

80 = 0.5*g3*6.92857^2

g3 = 3.333 m/s^2

d) Horizontal component of velocity Vx = V*cos(theta)

Vx = 40*cos30 = 34.641 m/s

total time of flight = Range / Vx

T = 450/34.641 = 12.99 s

Vertical component of velocity Vy = V*sin(theta)

Vy = 40*sin30 = 20 m/s

T = 2Vy/g4

12.99 = 2*20/g4

g4 = 3.079 m/s^2

e) v^2 - u^2 = 2*g5*H

61^2 - 0^2 = 2* g5 * 200

g5 = 9.3025 m/s^2

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