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 6.1 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 293.0 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 61.0 m/s. The projectile lands 257.0 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 410.0 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 54.0 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) initial velocity is Vo = 0 m/sec

height from which it was dropped is h = 80 m

time taken is t = 6.1 sec

Using S = (Vo*t) + (0.5*g*t^2)

80 = (0*t) +(0.5*g*6.1^2)

80 = 0.5*g*6.1^2

g = 4.3 m/s^2

b) given that initial velocity is Vo = 30 m/sec

Maximum height reached is Hmax = 293 m

Hmax = Vo^2/(2*g)

293 = 30^2/(2*g)

g = 1.53 m/s^2

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