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On the Apollo 14 mission to the moon, astronaut Alan Shepard hit a golf ball with a golf club improvised from a tool. The free-fall acceleration on the moon is 1/6 of its value on earth. Suppose he hits the ball with a speed of 28 m/s at an angle of 31° above the horizontal.

(a) How long was the ball in flight?
s

(b) How far did it travel?
m

(c) How much farther would it have traveled on the moon than on earth?

Answer :

IthaloAbreu

Answer:

a) 17.40 s

b) 417.6 m

c) 6.04 times farther

Explanation:

a) In the maximum height vy = 0, so:

vy = v0y + at

For the upthorwn, a= -g, because the movement occurs against free-fall, so the up time can be calculated:

0 = v0.sinα - g*t

α = 31º and sin31º = 0.515

g = (1/6)*10 = 1.66 m/s²

1.66t = 28*0.515

t = 8.70 s

The uptime is equal to downtime, so the total time is:

2x8.70 = 17.40 s

b) The distance that it travels is the x-axis, so:

D = vx*t, where t is the total time 17.40s

D = v0*cosα*t

D = 28*cos31º*17.40

D = 417.6 m

c) The uptime on Earth would be:

10t = 28*0.515

t = 1.44 s

The total time would be: 2.88s

So, the distance on Earth:

De = 28*cos31º*2.88

De = 69.12 m

So

D/De = 417.6/69.12

D/De = 6.04 times farther

a) The ball was in flight for 17.40 s

b) The ball travels 417.6 m

c) It would have traveled 6.04 times farther on the moon than on earth.

Given information:

initial velocity u = 28m/s

the angle of projection θ = 31°

acceleration due to gravity on the moon [tex]g\approx\frac{10}{6}m/s^2[/tex]

(a) at the maximum height final velocity [tex]v_y = 0[/tex],

where subscript y denotes vertical direction.

[tex]v_y = u_y - gt[/tex]

[tex]0 = usin\theta - gt\\\\usin31=gt\\\\1.66t = 28*0.515\\\\t = 8.70 s[/tex]

total time of flight is T = 2t = 17.40s

(b) The distance traveled

[tex]d =u_x \times T, \\d = u\times cos31\times T\\d = 28\times cos31\times 17.40\\ d= 417.6 m[/tex]

(c) The time taken to reach the maximum height on Earth would be:

[tex]10t = 28\times 0.515\\t = 1.44 s[/tex]

The total time of flight would be T' = 2.88s

So, the distance on Earth:

[tex]d' = 28\times cos31\times2.88\\d' = 69.12 m[/tex]

the ratio of the distances:

d/d' = 417.6/69.12

d/d' = 6.04

Learn more about acceleration due to gravity:

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