question in the description

Question

The height, h, in metres, of an object t seconds after it is dropped is h=-0.5gt²+k, where g is the acceleration due to gravity and k is the height from which the object is released. If an object is released from a height of 400m, how much longer does it take to fall to a height of 75m on the Moon compared with falling to the same height on Earth? The acceleration due to gravity is 9.8m/s² on Earth and 1.6/s² on the Moon.

Answer 1

Solve for t:

 

h = -(1/2)gt² + k

h-k = -(1/2)gt²

2(k-h)/g = t²

√(2(k-h)/g) = t

 

t_earth = √(2(400-75)/9.8) = √(325/9.8) = ____?

t_moon = √(2(400-75)/1.6) = √(325/1.6) = ____?

 

How much longer = t_moon - t_earth

Answer 2

75= -0.5(9.8)t^2 

t=3.912

 

 

75=-0.5(1.6)t^2

t=9.682

 

5.77