On the moon the acceleration due to gravity is 1/6 of Earth\'s. A ball is thrown

Question

On the moon the acceleration due to gravity is 1/6 of Earth's. A ball is thrown straight up on the moon and it takes t = 19 s to return to the surface.

25% Part (a) What is the numeric value for the magnitude of the free fall acceleration on the moon, gmoon in m/s2?

25% Part (b) Write an expression for the maximum height achieved by the ball on the moon, hm, in terms of the gravitational acceleration on earth, g, and the time, t.

25% Part (c) What is the numeric value for this height in meters?

25% Part (d) What is the difference in the maximum height of the ball when it is thrown on the Moon (hM) and the ball being thrown on the Earth (hE), assuming the same time of flight?

Explanation / Answer

here,

time of flight , t = 19 s

a)

the free fall accelration on moon , a = g/6 = 1.63 m/s^2

b)

let the intial speed be u

t = 2 * u /a

u = at /2

the maximum height , hmax = u^2 /2a

hmax = ((at)^2 /2^2)/2a

hmax = at^2 /8

c)

hmax = 1.63 * 19^2 /8 = 73.6 m

d)

the height on earth , he = 0 + 0.5 * g * (t/2)^2

he = 0.5 *9.81 * (19/2)^2 = 11.3 m

the difference in height , h = hmax - he = 57.7 m

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